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2021 104 Felipe Maciel Cardoso Strategic and Selfless Interactions: a study of human behaviour Director/es Moreno Vega, Yamir Gracia Lázaro, Carlos © Universidad de Zaragoza Servicio de Publicaciones ISSN 2254-7606 Felipe Maciel Cardoso STRATEGIC AND SELFLESS INTERACTIONS: A STUDY OF HUMAN BEHAVIOUR Director/es Moreno Vega, Yamir Gracia Lázaro, Carlos Tesis Doctoral Autor 2020 UNIVERSIDAD DE ZARAGOZA Escuela de Doctorado Programa de Doctorado en Física Repositorio de la Universidad de Zaragoza – Zaguan http://zaguan.unizar.es STRATEGIC AND SELFLESS INTERACTIONS a study of human behaviour felipe maciel cardoso October 9,2020 Felipe Maciel Cardoso: Strategic and Selfless Interactions: a study of human behaviour, © October 9,2020 Não sou nada. Nunca serei nada. Não posso querer ser nada. À parte isso, tenho em mim todos os sonhos do mundo. I am nothing. I will never be anything. I couldn’t want to be something. Apart from that, I have in me all the dreams of the world. — Tabacaria, Álvaro de Campos (Fernando Pessoa) À Zu, minha mãe, e à Amanda ABSTRACT Humans are unique animals, cooperating in scale unrivalled by any other species. We built societies composed of non-kins, and empirical results have shown that people have social-preferences and might be willing to perform costly actions in the benefit of others. On the other hand, humans also compete among themselves leading at times to negative outcomes, such as the overuse of Earth’s natural resources. Yet, competition between economic agents underlies the well functioning of markets, and its destabilisation – such as in an unbalanced distribution of market power – can harm trade efficiency. Accordingly, analysing how people cooperate and compete is of prime importance in the understanding of human behaviour, especially considering the impending challenges threatening the future welfare of our societies. In this thesis, we present works exploring people’s behaviour in social dilemmas – situations in which self-interested decisions are at variance with the social optimum – and in other strategic scenarios. Using the theoretical framework of game theory, their interactions take place in games abstracting these situations. Specifically, we performed behavioural experiments in which people played adaptations of common-pool resources, public goods, and other tailor-made games. Moreover, in an attempt to understand the existence of cooperation in humans, we propose a theoretical approach to model its evolution via a dynamics of heuristics selection. We begin by introducing the theoretical and empirical foundations in which this thesis is based upon, namely, game theory, experimental economics, network science, and the evolution of cooperation. Subsequently, we illustrate the practical aspects of performing experiments using software implementations. To understand people’s behaviour in collective action problems – such as climate change mitigation, which requires a global level of coordination and cooperation – we performed public goods and common-pool resources games among Chinese and Spanish participants. The obtained results provide some insights onto the variances and universalities of people’s responses in these scenarios. In this line, in recent years, individuals and institutions are increasingly concerned with social and environmental issues. Contributions in these scenarios, nonetheless, requires a substantial level of altruism by agents who have to make costly decisions. We performed two experiments to understand the drivers behind such decisions in two contemporarily relevant situations, namely, charity donations and socially responsible investments. Their results indicate that framing and v Figure 6.7Numerical results of the model. 116 Figure 7.1Illustration of the model for memory 1.122 Figure 7.2 Cooperation thrives at low mutation values. 126 Figure 7.3 Fraction of cooperative actions at the end of each generation. 127 Figure 7.4 Average cooperation at the stationary state. 128 Figure 7.5 Distribution of genes’ expressed values. 129 Figure 7.6Emerging Strategies. 132 Figure 7.7 Cooperation probability in one-shot games. 133 Figure 7.8 Evolution of heuristics with kin identification on LTT. 134 Figure 7.9 Evolution of heuristics with kin identification on RRN. 135 Figure 7.10 Cooperation probability in one-shot games for the model with the kin identification gene. 136 Figure a.1 Chinese participants manifested stronger individualistic propensities than their Spanish counterparts. 155 Figure a.2 Bootstrapping confirms the validity of the behavioral regression model. 159 Figure a.3 Performance of the behavioral regression model is statistically significant. 160 Figure a.4 Behavioral regression model is robust to misspecification. 161 Figure b.1 SD-betweenness determines payoffs but not posted prices. 164 Figure b.2 Extension of Figure 6.4of Chapter 6with the 50-nodes random network. 165 Figure b.3 Evolution of costs and prices for each experimental network. 166 Figure b.4Numerical results of the model. 169 Figure b.5Numerical results of the model. 170 Figure b.6 Numerical results of the model for networks with 50 and 100 nodes. 170 LIST OF TABLES Table 2.1Decision theory example 8 Table 2.2Prisoners’ Dilemma payoffs. 9 Table 4.1 Time-series analysis of the virtual forest’s state. 58 Table 4.2Targets in each session type. 60 Table 4.3Homogeneous sessions regression. 63 Table 4.4Heterogeneous sessions regression 64 xii list of tables xiii Table 5.1Number of participants in each cohort 75 Table 5.2 Regression results for the contributions to public goods. 78 Table 5.3 Regression results for the donations to charity. 80 Table 5.4 Random Effects regression with cluster robust standard errors at the individual level for the Forced Contribution phase. 82 Table 5.5 Random Effects regression with cluster robust standard errors at the individual level for the Keep in the Pocket phase. 83 Table 5.6Participants’ level of education 87 Table 5.7Country of Residence of participants. 88 Table 5.8Prior Knowledge 89 Table 5.9Questions and Framings. 93 Table 5.10 Framing of questions. 94 Table 5.11 Framing of multiple questions and fund profitability. 95 Table 5.12 Demographic variables impact. 97 Table 6.1Experimental results. 109 Table 6.2 Numerical results in experimental networks. 113 Table 6.3Numerical results for larger networks. 114 Table 7.1Memory variables and genes. 125 Table 7.2Pure strategies memory. 130 Table 7.3 Classification of heuristics according to their responses to the two pure strategies. 130 Table b.1Experimental results. 163 Table b.2Coefficients of the statistical models. 168 Table c.1 Dynamic panel model regression with cluster robust standard errors at the individual level. 172 Part I PRELIMINARIES 1 INTRODUCTION Detail from Stone Henge, Wiltshire, engraved by Robert Wallis, after J. M. W. Turner We are all apprentices in a craft where no one ever becomes a master. Ernst Hemingway, New York Journal-American This thesis is concerned with the behaviour of interacting agents. They live, have a noticeable cognitive capacity, and make decisions. Specifically, this thesis focus on the most intelligent and successful living beings that science knows so far: humans. Humans are ecologically dominant on the planet, having spread over diverse environments like no other species [1]. Driven by the struggle for survival in the harshness of the real world, humans conquered the earth by building unique societies of unrelated individuals [2], cooperating in a scale not rivalled by any other animal [3,4]. “To a large extent the future of the only place where life is known to exist is being determined by the actions of humans. Yet, the power that humans wield is unlike any other force of nature, because it is reflexive and therefore can be used, withdrawn or modified.” Lewis and Maslin [5] Humans don’t have to worry about predators anymore, although we are often worried about ourselves and our institutions. In this regard, contemporary societies endure challenges that are unique in history. Not because they harder or have worse consequences, such a statement cannot escape the realm of subjectivity. What is clear is that contemporary challenges are a result of, or are intensively affected by, the ever-changing Anthropocene [5]. In less than 0.01% of the time of earth’s existence, we have been able to alter the dynamics of ecosystems and even the whole earth climate [6]. Even if we end up extinct, our presence and influence on this planet will be available in the geological record for aeons [7]. At the time of writing, society is facing a global crisis as a pandemic propagates by the aether of connections we built in the last centuries. Even the resilience of our society depends on how we interact with our constructs and artefacts, as it is seen in the uncertainty associated with the effects of social media in the forms of government [8]. Whatever we have to face in the future, we need to understand how humans behave and how they respond to the forthcoming challenges. “We have created a Star Wars civilization, with Stone Age emotions, medieval institutions, and godlike technology.” Edward O. Wilson [9] In this regard, it is crucial to have in mind that humans, although unique in the animal kingdom [1,2], live in groups as other social animals and manifest behaviour which evolved both biologically and culturally while they interacted with themselves [10]. This resulted in individuals that sometimes have to be strategic but can also behave selflessly. Humans can selfishly compete for resources, but also can cooperate to reach a common goal [11] and even act altruistically in favour of others [12]. People have social preferences and might choose sub-optimal decisions for them for the benefit of another, yet they 3 4 introduction also have bias and prejudices and show favouritism towards their own group [13,14]. Those behaviours, moreover, can be influenced by environmental and cultural factors, by what people see, their culture, and the structures underlying their interactions [15–18]. Arguably, thus, identifying people’s decisions while interacting with others is chief for examining contemporary society’s current and imminent affairs. In this thesis, we present our work exploring the behaviour of humans in scenarios of competition, cooperation, and altruism. These interactions take place in games, a simple abstraction to study strategy and conflict among interacting agents [19,20]. We observe and analyse their behaviour through behavioural experiments and also explore models based on observed behaviour as well on theoretical hypotheses. Our goal is twofold, first to investigate human behaviour and increase our collection of people’s responses in strategic games and, second, to explore both emergence and implications of human behaviour in theoretical models. We begin in Chapter 2by providing a brief overview of the foundations of this thesis. As behavioural experiments are essential to this thesis, in Chapter 3, we summarise the methodology behind performing them. Subsequently, we present our work arranged in chapters according to their context, namely: collective action problems In Chapter 4, we discuss two collective action problems, namely public goods and common-pool resources, among participants from two countries. Section 4.1presents a social dilemma experiment in which participants gain profit by harvesting a virtual forest vulnerable to over-exploitation. In Section 4.2, we explore how information and the distribution of targets influence a collective risk climate-change dilemma game.You say you got a real solution Well, you know We’d all love to see the plan You ask me for a contribution Well, you know We’re doing what we can Revolution 1, The Beattles framing &altruism In Chapter 5, we present experiments exploring the influence of framing and information on donations and responsible investments. Section 5.1present experiments using multiple public goods with an associated donation. In Section 5.2, we present one experiment to understand the willingness of choosing impact investment options among experts and non-experts in this field. trading in networks In Chapter 6, we present an experiment exploring a generalization of the bargaining game in complex networks. Further, we propose a novel theoretical model based on the observed behaviour and discuss the results. a heuristic model of cooperation In Chapter 7, we expose a theoretical work attempting to answer the problems underlying cooperation in humans by using an original model of heuristics selection. introduction 5 Finally, we conclude in Chapter 8by summarising the findings of this thesis and exposing some prospective remarks. Necessary results that we deemed not sufficiently relevant to the main text are discussed in the Appendices 1. 1 Details of each experimental session were omitted for compactness, such as sociodemographic characteristics, instructions and ethical statements. They can be found in the supplementary materials of the corresponding publications. 2 FOUNDATIONS Cedalion standing on the shoulders of Orion from Blind Orion Searching for the Rising Sun by Nicolas Poussin. Let Pascal say that man is a thinking reed. He is wrong; man is a thinking erratum. Each period in life is a new edition that corrects the preceding one and that in turn will be corrected by the next, until publication of the definitive edition, which the publisher donates to the worms. Machado de Assis, The Posthumous Memoirs of Brás Cubas In this chapter, we present the theories and results forming the basis of this thesis. The reader might notice that the descriptions are brief and centre around the topics which are most related to our work, as these fields have a myriad of branches, and a thorough description would be out of scope. Nevertheless, they are sufficient for a proper comprehension of the next chapters. We begin by presenting the approaches by mathematicians in the fields of decision theory and game theory in Section 2.1. Subsequently, we detail results obtained in the field of experimental economics concerning human behaviour in games 2.2, and Section 2.4then describes some of the theories explaining the observed behaviour. As some of these findings and even our own of experimental work (Chapters 6and 7) requires a basic understanding of networks, we briefly introduce some of its theory in Section 2.3. Finally, we conclude in Section 2.5. 2.1 theories on decisions and games Pensées (“Thoughts”) by Blaise Pascal. In the 17th-century, Blaise Pascal published the Pensées, a collection of texts including the famous Pascal’s Wager wherein he provides an argument in favour of theism. In it, Pascal considers that humans bet their lives on the existence of God. If God exists, a true believer should receive an infinite benefit: salvation for eternity. Conversely, a nonbeliever would be doomed for eternity, an infinite punishment. If God does not exist, on the other hand, as humans live a finite life, humans can only receive a finite benefit, living without the constraints imposed by religion, or a finite loss, wasting their lives with the believer chores. Thus, humans are gamblers without the knowledge of God’s existence and obliged to bet in one option during their lifetime. His argument follows a probabilistic reasoning, by weighing expected value of each consequence the only rational choice would be to bet that God exists and live accordingly1. 1 This, of course, does not consider the problem of choosing the right deity to believe in, and of knowing what It would want from its believers. 7 8 foundations -it rains it does not rain Take the umbrella -1-1 Leave the umbrella at home -10 0 Table 2.1:Decision theory example. Illustration of utility values when deciding to take or not take the umbrella when going out. Pascal’s essay probably constitutes the first text on decision theory [20, 21], which studies how agents make decisions. It posits that agents have beliefs and desires and act rationally according to them. More specifically, their preferences determine a corresponding utility that will be maximized by rational decision-makers, i.e., they will consistently choose the option with the maximum expected utility value. When deciding involves uncertainty, it is often assumed that agents have a subjective probability distribution concerning the unknowns. As an illustration, imagine one person has to decide if she takes her umbrella with her when going out, carrying it implies a cost, although smaller than the cost of not having an umbrella if it rains. The utilities associated with each outcome in this example are described in Table 2.1. Agent’s decision will depend on their beliefs about the raining probability – e.g., if there is 0.5chance of raining, a rational decision-maker should take the umbrella with her. Decision theory reaches its boundaries when agents are interacting with others, and their decisions depend on the actions of other rational individuals. In these cases, the subjective probability distribution of one agent will depend on the decision-making process of the others it is interacting with, and vice-versa. In other words, the subjective probability distribution of one rational agent is an input of the distributions of all the others, leading thus to a system of equations. To solve such systems emerged the field of game theory, according to Roger Myerson, the essential logical fulfilment of decision theory [20]. In game theory, the word games refers to any situation of strategic interaction between self-interested parts. They are elementary components of social groups, as put by Colin Camerer: “a rough equivalent for social science of the periodic table of elements in chemistry” [15]. Games are abstract situations wherein involved agents, or players, obtain a benefit according to the combination of their actions; despite their simplicity, they provide a powerful framework to study real-world interactions. Game theory considers rational and intelligent players, the latter characteristic meaning that they can find the optimum decision if such exists [20]. Thus, if there is a mathematical solution to the decision-making problem, it will correspond to the agent decision. Commonly, studies focus on what is known as non-cooperative game theory, which deals specifically with the game 2.2 human behaviour in experiments 15 Proposers should offer the minimum amount possible (e.g., 1cent), while the Responders should accept any positive offer. Experiments, nonetheless, show that Proposers are willing to share significantly more than the minimum, with amounts usually being greater than Dictators’ offers [15]. This shows that, as Proposers are concerned with Responders rejecting their offer, they tend to propose higher values than Dictators. Therefore, these results provide a clear indication of the two essential features of people: being both strategic and altruistic. Importantly, people’s behaviour is affected by the specifics of the situations in which they are interacting. Besides, not everybody behaves equal [40] and changing the game structure and culture of the participants deeply affect game outcomes [15]. Experimental economics provides, therefore, one powerful paradigm to further uncover how people behave and why they behave as they do. As noted by Colin Camerer, “the goal is not to disprove game theory but to improve it, by establishing regularity, which inspires new theory” [15]. Knowledge obtained empirically can be used then to create new theories, which can be further tested by new experiments. This has been the case in our work presented in this thesis, such as described in Chapters 4and Chapter 6. In the following subsection we will briefly introduce the methodology behind experimenting in economics and illustrative experimental results of the Public Goods Game, as it relates the most to the work presented in this thesis 4. 2.2.1The methodology of experiments Alvin Roth [43] categorize economic experiments according to their goals in three types: i) Speaking to theorists: experiments with the goal of testing hypothesis originated from theory; ii) Searching for facts: experiments looking for new phenomena in settings with some modified situation; iii) Whispering in the ears of princes: experiments planned for policymaking. Initially experimental economics was mostly concerned with testing economic theory predictions, nowadays, however, it mostly concerns with testing how variations in the experimental setup can influence outcomes. This implies that experiments can lack an underlying rigorous theory and can be used to test informal hypothesis [30]; in other words, they would be searching for facts (ii). Notably, our experiments reported in this thesis fall on this category. Specifically, our experiments can be divided into two types: looking for differences in behaviour between different populations (Chapter 4); or looking for differences between two experimental treatments in the same population (Chapters 5and 6). 4See [15,41,42] for a broad overview of experimental economics results. 16 foundations 2.2.1.1The limitations of experiments Experimenters are often looking for phenomena that can be characterized qualitatively, as precise quantitative predictions are virtually impossible to be obtained [30]. Experimental conditions can have profound effects on the final result, being generally unfeasible to reproduce precisely data from previous experiments. This forces experimenters when testing a hypothesis to reproduce previous results to some extent; otherwise, it would not be feasible to distinguish the causes behind the observations. Specifically, results will depend on the specific context of each execution: its initial conditions (e.g., socio-demographic characteristics of the population), and the auxiliary assumptions about the experiments (e.g, the participants have understood the instructions). Therefore, an experimental conclusion obtained by evidence e , which supports or refutes a hypothesis H , is also determined by the initial conditions I and auxiliary assumptions K: (K∧I∧H) =⇒e(2.9) This implies that it is not only impossible to prove the general truth 5 of a hypothesis when e is observed, but also to refute it in a deductive approach when e is not observed. This is known as the Duhem-Quine problem, and it has direct implications when driving conclusions from experimental results. The controlled experiment enables the testing of hypothesis, but by being controlled it is far from the messiness of real-world interactions; hypotheses are not confirmed in isolation. Therefore, inferences have to be made with care when extrapolating experimental results. They are a valuable source of insights, but only can take us so far, as Guala puts it: “data – no matter how useful – cannot ultimately replace the evidence collected in the field” [45]. 2.2.1.2The case of Public Goods “Public goods and dilemma experiments are like using ping-pong balls; sensitive enough to be really informative but only with adequate control.”, John Ledyard [46] The Public Goods Game provides a good case study of how knowledge about human behaviour is obtained in the lab. Aside from being one of the most paradigmatic experiments in economics, it is connected to the majority of works presented in this thesis. Results from early experiments have shown that individuals would not free ride; they would contribute something to the public good. Generally, participants would be willing to contribute something between 40% and 60% of their endowment [46]. Nonetheless, if experimenters allowed the game to run repeatedly for some periods, contributions would eventually decay towards the Nash equilibrium [48]. This phenomena has sometimes been referred to as the overcontribution and decay and 5 According to the deductivist view [30,44], we never can confirm that H is true, only that it is false. Consequently, science would evolve by disproving false theories. 2.2 human behaviour in experiments 17 Figure 2.1:Experimental results of a repeated Public Goods Game, with and without punishment. Each panel shows mean cooperation at each time period. Top panel ( a ) shows sessions wherein participants started in the punishment treatment and the bottom panel (b) in a treatment without punishment. Figure from [47]. has been intensively replicated [30]. On one hand, the positive contribution shows again that humans tend to act pro-socially, on the other hand, the decay also demonstrates that this is not an unconditional tendency. One explanation for the decay phenomena is the impossibility of direct retaliation by participants, as withdrawing contributions will also impact non-free-riders. In this line, an experiment by Fehr and Gachter allowed participants to punish others after the contribution phase [47]. To assess the effect of punishment, they had to perform two treatments: one with, and one without punishment; the requirement of a controlled experiment. They observed significant differences between the two treatments: contributions were higher, and the decay was not observed when participants could punish, as shown in Fig. 2.1. This phenomena was connected with a new hypothesis concerning human pro-sociality [47,49,50], as we comment in Section 2.4. Nonetheless, these results have to remain constrained to a narrow laboratory scope until evidence is obtained in the field [45]. 18 foundations 2.3 structure:the sine qua non of interactions The Seven Bridges of Königsberg If we are to study interactions, we are obliged to understand the structure underlying them. One useful approach is to represent the interacting entities as vertices (nodes) of a graph (or network) and represent their connections as its edges (links), being this representation crucial for some of our work (Chapters 6and 7). Graph theory is a branch of mathematics considered to have begun with the work on the seven bridges of the Prussian city of Königsberg by the mathematician Leonhard Euler. In it, Euler mapped river islands and the bridges between them as the vertices and the edges of a graph, respectively. This representation allowed him to show that there was no path, more specifically no Eulerian path, that could visit each node (island) without visiting an edged (crossing a bridge) twice in the Königsberg bridges’ graph. Recently, this approach for modelling real systems as graphs have converged to the field of network science [51, 52], commonly referring to them as networks. a b c d A graph is usually represented by having its nodes as circles and edges as lines. In the social sciences, the first known use of networks to represent interactions between individuals is often attributed to the school mapping by Jacob Moreno [53], wherein he mapped interactions between boys and girls students in a sociogram. With this representation, focus on individuals was supplanted by a new holistic perspective: nodes as interdependent units connected by edges representing channels for the flow of resources, opportunities/constraints of interactions, or lasting relation between individuals [54]. This change in perspective gained more momentum in the 20th century as data from social and economic interactions [55] became available. Concurrently, different fields began to study the structure interactions of diverse type of systems, such as the world wide web [56], power grids [57], and protein networks [58]. Remarkably, properties from different types of systems could be explained by abstract and generic models [59,60], indicating that the underlying structure might have deep effects in the resulting phenomena, which is also the case for the systems studied here. Thus, we will introduce basic definitions from graph theory and the network models required for the understanding of our results 6. 2.3.1Graphs & Networks: Definitions and Properties A graph G= (V,E) is a structure composed of |V|>0 vertices (nodes) connected according to the set E={e1,e2, . . . } of edges (links). Commonly, graphs are represented by an |V|x|V| adjacency matrix A wherein each cell Ai,j=1 if there is an edge between vertex i and j , and Ai,j=0 otherwise. Moreover, if the edges have directionality – 6 For a general introduction on networks, see [61–63]. Moreover, [64] provides a summary of basic models properties, [54] gives an introduction of social networks, and [55] provides an introduction to the study of economic networks. 2.3 structure:the sine qua non of interactions 19 i.e., they are ordered pairs – G is denominated a directed graph, and an undirected graph otherwise. Each vertex has an associated degree k , which corresponds to the number of edges it belongs to: kv=∑ j∈VAv,j(2.10) If G is directed, the degree can be decomposed into the in-degree ( kin v ), edges arriving at v ; and the out-degree ( kout v ), edges outgoing from v: kin v=∑ j∈VAv,j(2.11)kout v=∑ j∈VAj,v(2.12) The average degree hki of a network is often used to characterize it. Moreover, different graph generating processes are expected to generate different degree distributions, i.e., a distribution such that P(k) corresponds to the probability of a randomly chosen vertex having degree k . Consequently, the empirical degree distribution often provides substantial information about the underlying mechanisms of the connections in a real network. 2.3.1.1Paths Networks often represent structures for traversal, as occur with transportation [65–68] and computer networks [69–71]. In other types of systems, distances between nodes might be also important as they can indicate the strength between the indirectly connected entities. In this regard, networks’ paths are one of their most useful attributes. A path corresponds to a sequence of distinct vertices such that each consecutive vertex pair corresponds to an edge in the graph. A similar type of sequence, without the vertex distinctiveness restriction, is called a walk and can consequently be infinite. The length of a path is given by the number of edges it traverses, namely, its number of vertices −1 . Most importantly, the distance ( d ) between two vertices is given by the minimum path length between them, which correspond to the length of the shortest path or the geodesic between them. Concerning the whole network, one informative metric is its average path length hdi , which corresponds to the average geodesic between all vertices pairs: hdi=∑V u6=vd(u,v) |V|(|V|−1)(2.13) 2.3.1.2Centralities One of the recurrent questions while studying networks concerns the individual importance of its vertices. Certain nodes can be critical for some process [72], and usually this can be seen by their position in the graph, i.e., by how central it is. Different metrics have emerged to 20 foundations measure vertices centralities according to the specific context, as the analysis described in Chapter 6. The most straightforward centrality metric corresponds to the vertices’ degree, despite simple it can nevertheless be very powerful, as the number of connections of a node is likely to be very informative of its role in the system. Some of the commonly used centralities metrics relevant to our work are 7: betweenness Betweenness centrality b measures how important a vertex v is, with respect to the possible paths between pair of nodes. Namely, it measures, the relative number of shortest paths a vertex belongs to: b(v) = |V| ∑ v6=s6=d σs,d(v) σs,d(2.14) This summation takes place for all pair of nodes without v , wherein σs,d(v) stands for the number of shortest paths between vertices s and d containing v , and σs,d to the total number of shortest paths between sand d. closeness Closeness centrality C measures how close a vertex is to all the other vertices. Specifically, it corresponds to the average distance to all the vertices of the graph, thus, a low value should indicate a more central vertex. It is given by: C(v) = ∑u∈Vd(u,v) n(2.15) 2.3.1.3Clustering If vertice a is connected to vertice b , and b is connected to vertice c , how likely is for a and c to be connected? In probabilistic terms, the answer would be always 1if all the connections were transitive, which would only occur in a complete graph. This is extremely unlikely to be the case in real networks, although they often exhibit some partial transitiveness. Transitivity can be measured by taking into account the fraction of times the relation (a,b)&(b,c) =⇒(a,c), i.e., the number of times the existence of a path of length 2implies a loop of length 3. Commonly, this will be done by calculating the graph’s clustering coefficient ( CC ), which corresponds to the number of closed triangles (3-vertices clique) for every path of length two, or triple: A loop of length 3or a3-vertices clique. CC(G) = 3|4(G)| |τ(G)|(2.16) Wherein 4(G) corresponds to the set of all closed triangles in G and τ(G)to the set of all triples in G. 7For a broader list of metrics, see:[63, Chapter 7] 2.3 structure:the sine qua non of interactions 21 2.3.2Graph models In this subsection, we introduce some mathematical models used to generate graphs. Here the reader might observe that one essential characteristic distinguishing graph models is their expected degree distribution or degree sequence. 2.3.2.1Erd˝os–Rényi Graph The Erd˝os–Rényi random graph, usually referred to as ER graph, was introduced by mathematicians Paul Erd˝os and Alfréd Rényi. In the ER model, a graph G(n,p) has n vertices connected randomly to each other with a probability p . As each edge occurs independently from every other, G is expected to have (n 2)p edges and its degree distribution is given by a binomial distribution of the form: P(k) = n−1 kpk(1−p)n−1−k(2.17) Wherein P(k) corresponds to the probability of a node having degree k . For large n , the distribution can be approximated by a Poisson distribution: P(k) = ehkihkik k!(2.18) As the probability of two vertices being connected is the same for every pair of vertices, a closed triple will be connected with probability p. In other words, the probability of being connected is given by: CC(G) = hki n−1(2.19) This implies that for large networks, the clustering coefficient tends to vanish. Real networks, nonetheless, tend to have a relatively large clustering coefficient, thereby demonstrating that connections do not occur randomly. On the other hand, the average path length in an ER graph tends to relatively small, such as is encountered in real networks: hdi ∼ lnn lnhki(2.20) 2.3.2.2Small-World Networks In 1967, Stanley Milgram published the result of a series of experiments in the social sciences, wherein participants were given an unknown recipient that should receive a letter sent by them [73]. As the target was a complete stranger, they were instructed to send the letter to one person they knew in the first name basis who should forward the letter following the same method. Remarkably, letters that reached 22 foundations Figure 2.2:Transition from a ring lattice to a random graph. For small values of p , a small-world regime exists, in which graphs will have a small average path length and a large clustering coefficient. Figure from [59]. the recipient had only been forwarded 6times on average. From this result emerged the notion of the “6degrees of separation”, in that we are only are 6steps away from every other person in the world; thus, we live in a small world. One compelling explanation of this phenomenon was published in 1998 by Duncan Watts and Steven Strogatz in one of the most influential papers in network science [59]. Their model starts from a regular ring lattice, in which every node is connected with their hki nearest neighbours, such as illustrated in the left graph of Fig. 2.2. Its edges are rewired according to a probability p , incrementing the disorder of the system as p grows. Thus, when p=1 a random graph is obtained, such as the right graph of Fig. 2.2. Interestingly, for small p>0 , the resulting graph has a small average path length, comparable with a random graph, but with a large clustering coefficient, as shown by the grey area of Fig. 2.3. This is a result of rewiring adding shortcuts to the graph, while the graph continues to be highly clustered as p is small, as illustrated by the middle graph of Fig. 2.2. 2.3.2.3Barabasi-Albert One important characteristic of real networks, not fully developed by the previous models, is their high degree heterogeneity. In real networks, some nodes can have significantly more connections than others, an unlikely result of a random process. Specifically, it has been observed that the degree distribution of some networks follows a power-law distribution [56,60,74,75] of the form P(k)∼k−γ , such that typically 2≤γ≤3 [63]. Interestingly, this type of distribution is scale-invariant, leading to such network being refereed as scale-free networks. The preferential attachment process is the most well-known explanation for such distribution [60]. It corresponds to a feedback-loop between connections, wherein nodes with high connectivity are more 2.3 structure:the sine qua non of interactions 23 0.00 0.25 0.50 0.75 1.00 10−5 10−4 10−3 10−2 10−1 100 p Figure 2.3:Average path length and clustering coefficient in WattsStrogatz networks. Normalized average path length (solid black circles) and clustering coefficient (open circles). Values correspond to a mean of 102of 103nodes networks. likely to obtain new connections. This proposal was firstly posited by “It is common in bibliometric matters and in many diverse social phenomena, that success seems to breed success.” Derek de Solla Price [76] Price in 1976 [76] by the name of cumulative advantage, explaining how highly cited research papers are more likely to be cited. Nonetheless, the work by Lazlo Barabasi and Reka Albert in 1999 [60] became the most famous using this approach. In their model, they consider a growing network, in which a node arrives with m new edges at each time step. It will connect those m edges to existing nodes in proportion to their degrees, a preferential attachment process, as coined by them. This will generate a network with a degree distribution following exactly P(k)∼k−3, as lustrated by Fig. 2.4. 2.3.2.4Configuration Model The configuration model was proposed by Béla Bollobás [77] to study graphs that have a degree sequence fixed beforehand. This allows specifying that every node has degree greater than zero, which is not possible with the ER graph. Moreover, it enables the specification of any degree sequence, being also useful for generating graphs with a power-law degree distribution without correlated degrees [78]. Given a fixed degree sequence ( k1,k2,··· ,kn ), it generates a graph according to the following algorithm: 1. Generate ∑n iki half-edges, wherein for each vertice i there is ki half edges connecting to it; 2. Randomly connects the pairs of half-edges to form an edge of the graph. Clearly, ∑n iki has to be even as ∑n iki=2|E| . This procedure does not guarantee that generation of a simple graph, as self-loops and 24 foundations 10−6 10−5 10−4 10−3 10−2 10−1 100 100101102103104105106 k P(k) Figure 2.4:Degree distribution in a scale-free network. Degree distribution of a network with 106 nodes generated by the Barabasi-Albert model, for m=5 [60]. The dashed line corresponds to a line with slope 3to guide the eye. multiple edges are possible. Nevertheless, both tend to relatively wane when n→∞ [64]. For the generation of networks following a powerlaw degree distribution it has been shown that, if the maximum degree is smaller than the square root of its size ( kmax ≤√n ), nodes’ degree will not be correlated [78]. random regular network Also known as a uniform random regular graph, it is a subset of the k-regular graphs, i.e, graphs wherein all nodes have the same degree k . It corresponds to a random graph generated by the configuration model by setting a fixed degree of k for every node. 2.4 explaining cooperation Previous sections have demonstrated that the initial predictions of game theory poorly predicted the behaviour of humans. People cooperated in experiments in which they should defect, they shared and donated money expecting no benefit from it. Indeed, humans cooperate in a unique scale, living in societies wherein trust and support among unrelated individuals are imperative [2]. Moreover, cooperation is also observed in the whole nature, from bacterias and cells to primates and other mammals [79]. This posed a challenge for evolutionary biology, as at first glance costly behaviour in favour of other individuals should not be selected [80]. As it turns out, cooperative behaviour can provide fitness advantages in certain conditions. In this section, we provide a brief description of the main explanations for the biological evolution of cooperation and in which conditions humans tend to cooperate. 3 PERFORMING EXPERIMENTS “There are two possible outcomes: if the result confirms the hypothesis, then you’ve made a measurement. If the result is contrary to the hypothesis, then you’ve made a discovery.” Enrico Fermi Plate 1,3from Charles Bargue’s Cours de dessin Behavioural experiments do not require a large apparatus to be performed, good research can be done with pencil and paper [127,128] or even with a bowl of beans [129]. Nonetheless, unless the specifics of the experiment require otherwise, it is preferred to run the experiment using a computer platform. In this way, session effects [130] due to experimenter influence and human mistakes are reduced. Moreover, non-computerized experiments are significantly more time consuming, especially if participants are playing in groups. For instance, in a repeated public goods game at the end of every round, the groups’ total contribution and participants’ payoff have to be calculated, which would be overwhelming if participants are not playing over a computer network. For the aforementioned reasons, all the experiments reported in the next chapters have been performed using a software platform. Specifically, excepting experiments reported in Sections 5.1 1 and 6.1 2 , all the experiments reported have been developed and performed by the author. 3.1 planning The first stage of an experiment usually is elaborating the ideas behind it, consolidating them in a practical setup. What scenario is intended to be reproduced or emulated in the lab? What hypotheses are going to be tested? What behaviour do we want to observe? After that has been decided, it is necessary to outline what are the requirements in terms of software and data. The former will determine how elaborated the system will have to be, and the latter how many participants and groups will be needed to have enough statistical power. Subsequently, it is necessary to prepare the instructions for the subjects explaining the experiment and start the software development process. Ideally, the project starts with a requirement analysis followed by the design of the software guaranteeing a clear structure and the possible reusability of the program [131]. 1It has been developed by the LINEX institute in Valencia. 2It has been developed by the software developers at the BIFI Institute. 31 32 performing experiments 3.2 developing The software for performing an experiment has several requirements: it needs a clear interface with understandable instructions; it has to manage groups of players playing simultaneously, synchronizing rounds through waiting pages; participants inputs have to be stored in a central database. This might seem rather daunting, fortuitously, however, reusability is spread in software development. The availability of code from people that confronted similar problems removes the burden of reinventing the wheel in every enterprise. In our case, almost all of our experiments were based on the oTree platform [132], which itself depends on several other free software, such as Django 3 , Bootstrap 4 and Redis 5 . In oTree, an experiment is structured according to the following nested components6: Session: structure corresponding to the experimental session, it is divided into a list of subsessions. Participant: entity corresponding to the participant playing the experiment, thus it references all the actions performed by her in the inner classes. Subsession: the elementary constituent of each session, usually it corresponds to one round in the game. Nonetheless, one round also might be fractioned into more subsessions. Group: structure containing a set of players, for instance, in public goods games each group of players with access to a common fund would be contained in a separate group. Player: stores the instance of play by the participant in one particular subsession. Thus, it allows for a participant to have different player roles in each subsession. For instance, in subsession A, the player can be the Proposer in an Ultimatum game, while in subsession Bshe will be the Responder. Page: the elementary division of a subsession, each page is visited by a player and constitutes one step of the experiment. Therefore, given that the core of the software requirements is already taken care of by oTree, most of the development consists in 3https://www.djangoproject.com/ 4https://getbootstrap.com/ 5https://redis.io/ 6 More details on how to develop an experiment with oTree are available at https: //otree.readthedocs.io/en/latest/index.html 3.2 developing 33 developing the specifics of the experiment: data modelling, configuration and layout of the pages, any calculus performed at each time step, control of participants sequence of play, translations (in the case of multilingual experiments), etc. Hence, most of the effort is generally spent with the experimental interface, which nonetheless can be very time-consuming. For instance, the forest representation displayed in the experiment presented in Section 4.1required the development of a library to control the map drawing and the resource states. The instructions also have to been developed carefully, it should state in clear and simple sentences what the experiment is about and provide a tutorial on how to play the game. As an illustration, we display below the instructions of the experiment presented in Chapter 6. 34 performing experiments Instructions Thank you for participating in this experiment, that is part of a research project in which we try to understand how individuals make decisions. You re not expected to behave in any particular way. At this moment the experiment begins. Please keep quiet until the end, turn your cell phone off, and remember that the use of any material foreign to the experiment is not allowed (including pen, pencil or paper). Your earnings will depend on your own decisions and those of the other participants. Additionally, you will receive 5 efor participating in the experiment until the end. Please keep quiet during the experiment. If you need help, raise your hand and wait to be assisted. Please do not ask any question aloud. You participate along with other people with whom you interact according to the rules explained below. The session lasts about an hour and a half. The following instructions are the same for every participant of this experiment. Once completed the session, you will receive 5 efor participating, along with your earnings corresponding to the rounds, once converted into euros. For convenience, the total earnings are rounded up to the nearest 50 cents. You will access the experiments after reading these instructions. When all participants have accessed, the rounds will begin. You are going to participate in 4 experiments. Each experiment consists of 15 rounds. Before starting each experiment, all the players, you included, will be randomly located in the nodes of the network shown below. 3.2 developing 35 Your position in the network will be denoted with the letter ‘M’ (for me). In the same way, two different nodes will be chosen as Source (S) and Destination (D) respectively. Their position in the network will be denoted with the letters ‘S’ and ‘D’. All the players will remain in the same position during each experiment of 15 rounds. In the same way, the source and destination will remain in the same position throughout each experiment of 15 rounds. The players will play the role of intermediaries. A good must be transported from Sto Dgenerating a benefit of 100 tokens for all players involved (S,D, and all nodes in the path between them). Intermediaries (that is, the players) simultaneously have to post the fraction of these 100 tokens they would like to charge if selected, which must be between 0 and 100 tokens. You will have 60 seconds to post your price. If you do not post a price, the computer will decide for you: please do not run out your time and make your own decision. This is the screen you will see in the first round (this screenshot is only an example): Round 1 of series 1 The sum of prices along any given path between Sand Ddetermine a total cost. Once all the intermediaries have posted a price, the cheapest path (with lowest total cost) from Sto Dwill be selected. If the total cost of the cost cheapest path is less than or equal to 100 tokens, the good will be taken from Sto D. Otherwise, that is, if all the paths from Sto Dcost more than 100 tokens, there will be no deal and no value will be generated. Ties are broken randomly, that is, if there are more than one cheapest path, one of them will be selected at random. 36 performing experiments Your payoff in this round will be: a) If you are located on the selected cheapest path, you will receive your price as payoff. b) Otherwise, that is, if you are not on the selected path, you will not receive any payoff in that round. S and D will receive, equally distributed, the rest of the 100 tokens. From the second round on, you will be informed about whether there was a deal in the previous round, and if so what was the selected cheapest path, and the costs of this path. You will also be informed about the cheapest path through your node regardless of whether this was the selected cheapest path. The selected path will be highlighted by a dashed red line, while the cheapest path through your node will be highlighted by a blue solid line. Note that the cheapest path through your node may contain loops, i.e., it may pass more than one time through some nodes. With this information on the screen, you must set a price for the current round. At the end of each experiment, the positions of all players, the source, and the destination will be randomly reassigned, and a new experiment of 15 rounds will begin. This is the screen you will see in the subsequent rounds (this screenshot is only an example): Round 4 of series 1 Please, click the below NEXT button to start: [NEXT] 3.3 testing &fixing 37 3.3 testing &fixing “All code is guilty, until proven innocent.” Anonymous author When a first version of the experimental software is ready, it has to be tested several times for finding possible programming errors or misspelled text. Testing can generate new ideas or the recognition of new demands, which will be inserted into a new version. This loop repeats until software is recognized to be ok. Hopefully, the final version will be bug-free. 3.4 running Lastly, a batch of experiments will be planned and participants will be recruited for the sessions. Ideally, a pilot is initially programmed with a small subset of participants to verify if some change in the experimental setup would be needed or beneficial for the experiment. In our work, most of the times, we recruited participants through the volunteer pool of the IBSEN project (http://www.ibsen.eu), which, at the time of writing, contains 28234 registered participants. Participants have to sign an informed consent to participate, besides their anonymity is always preserved in the experiment. Moreover, the call for participants will occur only after it has been checked and approved by a research ethics committee, ensuring the procedure is performed following the relevant guidelines and regulations. Furthermore, monetary incentives are used to motivate participants, and they are directly tied to their performance in the game. Given that we are not able to observe their other intrinsic preferences, it is reasonable, ceteris paribus, to assume they prefer a larger payoff over a smaller one. This procedure follows the methodology of paying participants from experimental economics, which is at variance with some other fields, such as experimental psychology 7 . This practical detail will nonetheless constrain the number of participants, as an experimental budget is limited. Usually, payment per subject is calculated such that the average payoff is around the country average hourly wage. Accordingly, at the end of the experiment participants will be paid in cash in the case of a lab experiment, while in online experiments payment is often done by using an external service such as PayPal8. In a lab experiment, people can enrol through open calls in the IBSEN recruitment platform, and they are instructed to attend at a scheduled time and place. As some people might not be able to attend, participants are usually over recruited. Unfortunately, depending on the experimental setup, extra participants might not be able to play, in this case, they will be paid the game expected payoff and be offered apologies. It is not a perfect solution, but still better than not perform7See [30, Chapter 11] for an overview and discussion in this subject. 8https://www.paypal.com/ 38 performing experiments ing the session. Participants are often paid according to a show-up fee (a fixed amount guaranteeing that they receive at least something) plus some quantity in the function of their earnings in the game. Experiments can also be performed online, with each participant accessing the platform remotely. This approach reduces controllability of the experiment but allows a higher flexibility in the number of participants. As participants’ efforts are reduced (they can play from their homes for just some minutes), the payment can follow a lottery, such that only some fraction of the players will be paid some substantive amount. Hence, by this approach, there is virtually no limitation in the maximum number of participants. Nonetheless, participants probably do not have the same incentives as when paid directly by their earnings in the game. Thus, to motivate them, the lottery selects winners in proportion to their performance in the experiment. The main issue with online experiments is that, unfortunately, it is not trivial to synchronize play among participants, which makes repeated games hard to be performed, although some solutions are possible [133]. When all the experimental sessions have been performed, backup copies of the experimental data are made. The next steps are preprocessing and analysing the data, which will generate results such as the ones presented in the following chapters. Part II EXPERIMENTS AND THEORETICAL MODELS 4.1 a common pool of dynamic resources 47 of the no-recovery threshold. Nonetheless, the forest’s state could be monitored at all times via a detailed interface (Fig. 4.2). Participants could also compare their own performance in terms of effort, yield, and profit with others. Using this setup, we performed experimental sessions in two pool of participants: i) 96 undergraduate students in Xi’an, China; ii) 90 individuals from the general population in Zaragoza, Spain. Participants were instructed that they would receive a monetary payoff tied to their end profit in the game. The resulting payoffs amounted to an average of U 62.6in China and e 15.1in Spain, further details are shown in a. Figure 4.2:Screenshot of the gameplay page . We divided the gameplay page into three distinct parts: resource state,performance review, and decision making. The resource state part consisted of a gamelike visualization of the virtual forest plus a status (resp., progress) bar showing the number (resp., fraction) of remaining trees. The performance review part focused on effort, harvest, and profit bar charts with a hover effect such that moving the cursor over any of the bars triggered a tool tip displaying the corresponding numerical value. Lastly, the decision-making part comprised a simple input form asking for the desired effort and a message box that automatically converted effort into the harvesting cost. Final decisions had to be confirmed by clicking the Next button. For the actual sessions of the experiment, we used Chinese or Spanish translations. 48 collective action problems 4.1.3Results We used the MSY value as natural performance classifier for 16 Chinese and 15 Spanish player groups. Namely, we defined the optimal exploitation as any number of trees left for cutting after 50 rounds that was within ± 10% of the MSY number (136–166 trees). Only one group from each of the countries was able to optimally exploit the resource. None of the groups underexploited the resource by ending the experiment above the optimal range, whereas a total of 14 Spanish and 15 Chinese groups overexploited the resource by ending below this range. The virtual forest’s time evolution suggests that the former groups performed much worse (Fig. 4.3A). Seven groups from Spain drove the number of trees in the forest below the no-recovery threshold ( = 100 trees), whereas only one group from China did the same, and it did so only in the last round of the game. Nevertheless, a time-series regression analysis reveals that multiple Chinese groups kept depleting the resource, and given more time, would have likely crossed the no-recovery threshold too (Fig. 4.3B). Denoting with Rt the virtual forest’s state at time step t , where t0= 20 ≤t≤50 , we fitted the following model to the time-series data pertaining to the groups who overexploited, but did not deplete the resource. Rt=c0+c1(t−t0)+(1+c2)Rt−1+c3(Rt−1−Rt−2)(4.5) Parameters c0 , c1 , and c3 correspond to the constant, the trend, and the auto-regressive term, respectively. Parameter c2 reflects time series stationarity. The results for the Sustained groups are shown in Table 4.1. Six additional Chinese groups, , but none of the Spanish groups, kept depleting the resource ( c1<0 ) until the end of the experiment. Given more time, these groups would have likely crossed the no-recovery threshold. A total of seven groups on each side sustained the overexploited resource, i.e., their exerted effort was sustainable, but they kept earning suboptimal profits (Fig. 4.3C). Interestingly, none of the groups managed to fully reverse the decline and finish with a recovering resource ( c1>0 ). A conclusion is that the outcome in both countries, especially when considering together the groups who kept depleting or already depleted the resource (red rectangle in Fig. 4.3C), was remarkably similar and rather dismal. 4.1.3.1Behavioural Model To understand how participants were behaving in the experiment, we constructed a statistical regression model of participants behaviour. The model’s dependent (i.e., response) variable was effort, which 4.1 a common pool of dynamic resources 49 0 100 200 300 400 Round Resource Optimal Overexploiting Depleted China 100 125 150 175 200 Round Resource 20 A Spain Spain China 30 40 50 20 30 40 50 Underexploited Optimal Overexploited Recovering Sustained Depleting Depleted China Spain 20 30 40 50 10020 30 40 50 100 Depleting Sustained B C Figure 4.3:Overexploitation is a trend. A, Out of 16 Chinese and 15 Spanish groups who exploited the common-pool resource, only one group from each country was able to keep the resource at an optimum. We defined the optimum as ± 10% from the number of trees maximizing the sustainable yield ( ≈ 151 trees). Worryingly, all other groups overused the resource, and what is more, one Chinese and seven Spanish groups depleted it below the no-recovery threshold ( = 100 trees). B, Chinese groups seemingly do better than their Spanish counterparts, but is this truly so? To examine the likely fate of overexploited, but non-depleted virtual forests beyond round 50, we tested whether after a transitory period of about 20 rounds the number of trees was recovering, sustained, or depleting (Table 4.1). We found that six Chinese groups kept depleting the resource until the very end, while seven groups from each country sustained a relatively constant number of trees. No groups from either country managed to overturn the negative trend and allow the resource to recover. C, Notably, none of the groups from the two countries underexploited the resource, while a total of seven groups from each country depleted or would have likely ended up depleting the resource (red rectangle). we tried to explain using following independent (i.e., explanatory) variables: •The virtual forest’s state : we expected participants to exhibit different behaviours when the resource is abundant as opposed to when the resource is depleted. 50 collective action problems •Lagged own efforts : included to account for potential autocorrelations in the play of individual participants; positive autocorrelations, in particular, would be an indication of decision-making “inertia” whereby high (resp., low) past efforts increase the likelihood of high (resp., low) present effort. •Lagged average efforts of others : included to account for potential cross-correlations as a reflection of mutual influences between participants. Model parameters, i.e., regression coefficients, accompanying these three types of explanatory variables were kept constant among participants from a given country, thus characterizing a collective behavioural focus. Individual differences entered the model by allowing constant terms and residual variances to be participant-specific via fixed effects, and via participant-specific residual variances, respectively. We interpreted the former as individualistic propensities to exert effort irrespective of the state of the explanatory variables. Accordingly, players with larger fixed effects were more likely to cut trees even if the number of trees left for logging was small, or even if other players refrained from logging. Residual variances, by contrast, quantified individualistic propensities to randomly vary effort. We introduced participant-specific residual variances because we expected that human participants would exhibit a wide spectrum of behaviours. With these ideas in mind, a general model formulation was Ti(t)=βRR(t)+ S1 ∑ s=1 β−s TTi(t−s)+ + S2 ∑ s=1 β−s hTihT(t−s)i+βi+ei(t), (4.6) where dependent variable Ti(t)corresponds to the ith player’s effort in round t . Among the three types of explanatory variables, R(t) is the virtual forest’s state in round t , Ti(t−s) is the i th player’s lagged effort s rounds prior to t , and hT(t−s)i is the lagged average effort of others, also s rounds prior to t . The numbers of lagged terms in the model, S1 and S2 , were unknown prior to parameter estimation. Quantity βi is the model’s constant term, i.e., a fixed effect specific to the i th player. Finally, ei(t) are the model’s normally distributed residuals with zero mean and residual variance σ2 i , again specific to the i th player. Assuming the normal distribution here implied a lack of autocorrelative structure in residuals. This was reasonable given that the lagged own efforts in Eq. (4.6) should account for potential autocorrelations in player decisions. The model is able to explain the posted efforts. Fig. 4.4shows that predictions fit observations well as it is seen in observation-vsprediction scatter plots: points gather around the “diagonal”, i.e., the 4.1 a common pool of dynamic resources 51 -2 -1 0 1 2 -2 -1 0 1 2 Standardised observations Predictions -2 -1 0 1 -2 -1 0 1 Predictions A B China Spain Standardised observations Figure 4.4:Behavioural regression performance. Observation-vs-prediction scatter plots and the accompanying statistics intuitively display and quantify the performance of statistical regression models. In such plots, the scattered points should group around the “diagonal”, meaning that the line fitted to these points should be statistically indistinguishable from the line with intercept 0 and slope 1 . A, For the Chinese data, the intercept is indeed indistinguishable from 0(estimate -0.0018;95% CI [−0.0221,0.0186] ), but the slope is slightly lower than 1(estimate 0.9544;95% CI [0.9279,0.9809] ), thus suggesting that the model somewhat overpredicts (resp., underpredicts) low (resp., high) efforts. The coefficients of determination is R2=0.592 . B, For the Spanish data, these minor performance issues disappear because not only the intercept is indistinguishable from 0(estimate -0.0006;95% CI [−0.0193,0.0180] ), but also the slope is indistinguishable from 1 (estimate 0.9888;95% CI [0.9659,1.0116] ). The coefficients of determination is R2=0.689 . Due to a large number of data points ( > 4000 per plot), we grouped them into bins as evenly as possible, and then displayed the medians (circles), the interquartile ranges (boxes), the limits that would encompass 99.3% of normally distributed data (whiskers), and “outliers” (individual points). line with intercept 0and slope 1. The coefficients of determination further indicate that the model accounts for nearly 60% (resp., 70%) of the total variance in the Chinese (resp., Spanish) data. The behavioural regression model offers plausible explanations on why outcomes in China and Spain were similarly dismal. We found among the Spanish participants that, while the virtual forest’s state and the average effort of others inform decisions on the current effort, a key determinant in this context is one’s own lagged efforts (Fig. 4.5A). We thus witnessed a form of decision-making “inertia” by which past choices heavily weigh on the present choice. The effect is significant up to five lags in the past. Interestingly, the Chinese participants exhibit qualitatively the same behavioural patterns; again the forest’s state and the average effort of others inform decisions, but these are much less influential than one’s own lagged efforts (Fig. 4.5B). Even quantitatively the results are remarkably similar because only the effect 52 collective action problems 0.0 0.1 0.2 0.3 0.4 0.5 Parameter values Spain -1 -2 -3 -4 -5 -1 RTTTTT⟨T⟩ -0.2 -0.1 0.0 Adjustments China A B βββββββ Δ Δ Δ Δ Δ Δ Δ -1 -2 -3 -4 -5 -1 RTTTTT βββββββ ⟨T⟩ Figure 4.5:Behavioural patterns behind the demise of the commons are robust across nations. A, Estimated parameter values show that while the virtual forest’s state (parameter βR ) and the effort of others (parameter β−1 hTi ) inform participant decisions, the Spanish participants exhibit a form of decision-making “inertia” by which the current effort strongly reflects previous own efforts (parameters β−1 T to β−5 T ). The effect is significant up to five lags in the past. Here, shown are the parameter estimates (points) and the corresponding 95% confidence intervals (error bars). B, Adjustments of the Spanish parameter values to fit the data from China indicate that the Chinese participants exhibit the same decisionmaking “inertia” as their counterparts in Spain. The effect is only slightly weaker at lag 2(parameter ∆β−2 T ), but otherwise statistically indistinguishable between the two countries. The effort of others also has a statistically indistinguishable effect. The only qualitative difference is reflected in the ∆βR parameter, revealing that the Chinese (resp., Spanish) participants exert more effort when the resource is scarce (resp., abundant). This is consistent with a gentler (resp., steeper) initial decline of the resource in China (resp., Spain). The negative relationship between resource abundance and effort in China backs up our conclusion from the time-series analysis (Table 4.1) that six additional Chinese groups would have eventually depleted the resource. of own effort at lag 2is slightly weaker among the Chinese participants, while the effect at other lags is statistically indistinguishable between the two countries (Fig. 4.5B). The same is true for the average effort of others. Based on these results, one conclusion force itself upon us. Given that a decent number of participants from vastly different countries performed in a remarkably similar fashion, behavioural patterns behind the demise of the commons are, if not universal, then at least robust to a myriad of confounding factors. 4.1 a common pool of dynamic resources 53 The one substantial difference between the two countries is that the virtual forest’s state correlates negatively with the effort of the Chinese, but positively with the effort of the Spanish participants (Fig. 4.5). The former start exploiting the resource more cautiously, but then compensate for a steady resource degradation with more effort. The latter, by contrast, start more aggressively, but then curtail their zeal in response to a disappearing resource. The described difference between the two countries helps to explain the faster resource depletion in Spain than in China (Fig. 4.3), and is fully consistent with the clustering results (Fig. 4.7). Analysing the participant-specific model terms further complements this explanation (Appendix Section a.1.1). Meticulous regression diagnostics show that we avoided the common pitfalls of this type of analysis, and thus that the model’s results are credible (Appendix Section a.1.2). 4.1.3.2Clustering To gain a deeper insight about the differences among participants from both countries, we resorted to the k -means clustering algorithm. We used four quantitative characteristics as a basis for clustering with the idea that these characteristics would reflect behaviours exhibited in each of the two halves of the game experiment. They are cumulative efforts and total profits from both the first and the second half of the game taken separately. We surmised that behavioural changes between the two game halves would be of particular interest given that the resource state deteriorates as time passes, causing profits to decline as well. In such an analysis, the optimal number of clusters into which the dataset should be partitioned is not a priori known. As many as 11 different optimality measures for addressing this problem are commonly found in literature [170]. Among these, we selected the silhouette method for its conceptual clarity [171]. The silhouette method contrasts cluster cohesion (i.e., how similar data points are to their respective clusters) to cluster separation (i.e., how dissimilar data points are to other clusters). The larger the average silhouette value of the dataset depending on the number of clusters, the better is the given partitioning into clusters. Using the silhouette method on Chinese and Spanish data separately, we first found that the Chinese participants are best partitioned into three clusters (Fig. 4.6A). The Spanish case is somewhat ambiguous because partitioning into two clusters yields only a marginally larger average silhouette value than partitioning into four clusters (Fig. 4.6B). A closer inspection of both options reveals that the results are more informative in the context of our game experiment when the Spanish participants are partitioned into four clusters. The Chinese participants exhibit three prominent behaviours broadly describable as aggressive, moderate, and timid (Fig. 4.7A). Effort and 54 collective action problems B Optimum Local maximum 0.4 Optimum Avg. silhouette width 0.3 0.2 0.1 0.0 0.4 0.3 0.2 0.1 0.0 1 Number of clusters 2 3 4 5 6 7 8 9 10 Number of clusters 1 2 3 4 5 6 7 8 9 10 A China Spain Figure 4.6:Determining the optimal number of clusters with the average silhouette width. The silhouette value is a measure of how well a data point fits to its own cluster as opposed to other clusters (cohesion vs. separation), ranging from -1for a poor fit to 1for a good fit. Averaging silhouette values over an entire dataset produces an aggregate measure, called the average silhouette width, of how well the data have been clustered. This measure is a function of the number of clusters. The best clustering is achieved with the number of clusters for which the average silhouette width is maximal. A, For the Chinese data, the optimal number of clusters is three. B, For the Spanish data, partitioning into two or four clusters yields nearly an equal average silhouette width. We opted for the latter number because four clusters proved to be very informative in the context of our game experiment. profit gradually decrease from aggressive to moderate to timid players. Remarkably, performing independent clustering on the Spanish data reveals considerably similar behaviours patterns, with the addition of a fourth one, dubbed flipping (Fig. 4.7A). This last behaviour is aggressive or moderate in the first half of the game, but turns timid in the second half. We furthermore found that aggressive and timid behaviours are almost equally abundant in both countries, encompassing ≈ 25% and ≈ 10% of players, respectively (Fig. 4.7A). The Chinese case is enough to demonstrate that with such a distribution of players overexploitation is the most likely outcome. Adding the rather aggressive first-half behaviour of flipping players to this only contributes to the faster resource decline in Spain than in China, thus helping to explain why multiple Spanish groups managed to even cross the no-recovery threshold. Prominent player behaviours show what separates optimal harvesting from sustained overexploitation from resource depletion. Groups who harvest optimally have almost the same composition in both countries (Fig. 4.7B), characterized by a relative scarcity of aggressive ( ≈ 17%) and a disproportional abundance of timid ( ≈ 33%) players. Groups responsible for sustained overexploitation also have almost the same composition in both countries (Fig. 4.7B), only here aggressive players are abundant ( ≈ 30%) and timid players are scarce ( ≈ 7%). The Chinese group who depleted the resource has the highest proportion of aggressive players ( ≈ 33%) and no timid ones whatsoever (Fig. 4.7B), while the corresponding Spanish groups have only a few stray timid players ( ≈ 2.5%). The latter groups also harbour almost all flipping 4.1 a common pool of dynamic resources 55 0.6 1.2 1.8 Cumulative China Spain A G G R E S S I V E M O D E R A T E T I M I D F L I P P I N G E1 A M T F ggressive oderate imid lipping A Effort (1 half) st Effort (2 half) nd Profit (1 half) st Profit (2 half) nd E2 P1 P2 E1 P1 E2P2 E1 P1 E2P2 E1 P1 E2P2 E1 P1 E2P2 E1 P1 E2P2 E1 P1 E2P2 E1 P1 E2P2 China Spain Fraction 0.00 0.25 0.50 0.75 1.00 Optimal Sustained 0.00 0.25 0.50 0.75 1.00 Depleted Spain 0.00 0.25 0.50 0.75 1.00 Optimal Sustained Depleted Depleting China B Figure 4.7:Interplay of prominent behaviours explains overexploitation. A, Running a clustering algorithm on data from China and Spain separately, we identified three (resp., four) distinct prominent behaviors among the Chinese (resp., Spanish) participants. Apart from the behavior unique to Spain, the three remaining behaviors are nearly identical irrespective of the country. In terms of effort, these can be described as aggressive, moderate, and timid. With the scale set relative to the MSY effort and the corresponding profit, we see that aggressive players exceed the MSY effort by over 80%, earning large profits in the first half of the game. Moderates stay closer to the MSY effort, nonetheless exceeding it by about 20%. Timid players start cautiously at 60% of the MSY effort and, unlike aggressive or moderate players, reduce effort in response to resource deterioration. The fourth Spanish behavior flips from an aggressive initial stance to a timid subsequent one, earning almost no profit late in the game. B, Overall abundance of aggressive and timid players is remarkably similar across countries (left panel), as is the abundance of these players in groups that played optimally and groups that sustained the resource in an overexploited state (middle and right panels). Optimal play clearly requires a much more favorable aggressive-to-timid ratio than is present in the overall abundance, thus explaining overexploitation. The flipping behavior is nearly exclusive to groups that depleted the resource in Spain, indicating that many players become responsive to the resource state only when it is too late. players ( ≈ 45%), who act rather aggressively in the first half of the game and contribute to resource decline alongside aggressive players 56 collective action problems ( ≈ 21%). The four identified prominent behaviours thus go a long way in explaining the subtle differences in the virtual forest’s time evolution between China and Spain, as well as the overall bias towards overexploitation. Particularly intriguing is a number of remarkable similarities between the two countries hinting at the existence of robust behavioural patterns behind the demise of the commons. 4.1.4Discussion Having asked participants from China and Spain to exploit a virtual forest while facing the same epistemic and socio-economic obstacles as real-world operators, we found that seemingly different outcomes are, in fact, remarkably similar and bode ill for the fate of common-pool resources. An exploratory data analysis in the form of clustering reveals that the results are largely attributable to three behavioral types (also called phenotypes in the literature), dubbed aggressive, moderate, and timid. Although the nature of the game in our experiment is different from those in previous experiments that report behavioral phenotypes [172–174], we see clear parallels between aggressive, moderate, and timid players herein and defectors, cooperators, and supercooperators in Ref. [174], respectively. The consistency of previously identified behavioral phenotypes [173,174] further suggests that the types we found are also a consistent feature of human behavior rather than a peculiarity of the specific experimental setup. In fact, having worked with two geo-socially distant populations, and in a novel and relatively complex context, our results go a long way in fortifying the conclusions of the cited studies that human behaviors in social dilemmas are divisible into a small number of stable phenotypes. A previous study [175] using a similar setup, albeit with explicit resource “dynamics” such that every 10 standing trees yielded one new tree per round, reported the outcome of the game experiment compared to other situations. Here, by contrast, we implemented a more realistic dynamic—whose qualitative characteristics, but not quantitative details, are known by the participants—and identified collective behavioral mechanisms that underpin decisions on exploitation, thus pointing to one main culprit for similarly dismal outcomes in both countries. Instead of prioritizing the resource state when deciding the current effort, participants operate under decision-making “inertia” by which they are much more concerned with their own past efforts. A surprising aspect here is that this mechanism materializes in two populations not only separated geographically, but also influenced by a myriad of confounding factors such as age, education, and culture. The Chinese participants shared comparatively young age, exposure to higher education, and upbringing in the midst of a quintessential East Asian cultural heritage. The Spanish participants mirrored the general population in terms of age and educational background, while 4.2 targets and biases:a collective-risk social dilemma between two countries 63 Dependent variable: Player Contribution Spanish 0.036 (0.030) Informed −0.081∗∗ (0.033) LT 0.010 (0.021) Round −0.009∗∗∗ (0.003) Informed x Spanish 0.081∗(0.043) LT x Spanish −0.053∗∗ (0.027) Constant 0.558∗∗∗ (0.027) Observations 1,920 R20.018 Adjusted R20.015 F Statistic 35.875∗∗∗ Note: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01 Table 4.3:Homogeneous sessions regression . Estimates from a random effects model for the Homogenous sessions’ participants. Robust standard errors are clustered at the individual level. ˜ Cit =β0+β1Informedi+β2Spanishi+ β3Informedi∗Spanishi+ β4LT40 +β5LT40 ∗Spanishi+ β6Roundt+ αi+eit (4.8) In this case, ˜ Cit corresponds to the normalized contribution and LT40 is a dummy variable controlling for the target of the participant’s group ( LT =20 is the reference group) – i.e, it equals to 1in the LT40 treatment and 0 otherwise. The results of the regression for the Homogeneous and Heterogeneous sessions are shown in Tables 4.3and 4.4, respectively. The decay in contributions with time is common to both session types, as generally it is observed in repeated Public Goods Games [46,48]. In the homogeneous sessions, Chinese participants contributed less when information of Spaniard’s nationality was disclosed (-0.08 in contributions per round). Interestingly, this effect is not observed for Spanish participants (0=0.08-0.08), and although their contributions are smaller when their group had a local target, they were still around 64 collective action problems Dependent variable: Normalized Player Contribution Spanish 0.102 (0.150) Informed 0.021 (0.072) (LT =40)−0.162∗∗∗ (0.035) Round −0.035∗∗∗ (0.008) Informed x Spanish −0.084 (0.136) (LT =40)x Spanish −0.152∗(0.084) Constant 1.314∗∗∗ (0.083) Observations 1,920 R20.056 Adjusted R20.053 F Statistic 112.892∗∗∗ Note: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01 Table 4.4:Heterogeneous sessions regression . Estimates from randomeffects regression for the Heterogeneous sessions’ participants. Robust standard errors are clustered at the individual level. 4.2 targets and biases:a collective-risk social dilemma between two countries 65 One Target Two Targets Uninformed Informed 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 0.0 2.5 5.0 7.5 10.0 0.0 2.5 5.0 7.5 10.0 Mean Contribution by Participant China Spain Figure 4.9:Distributions of players’ average contribution in the Homogeneous sessions. Histogram of players’ mean contributions according to the information provided and treatment in the Homogeneous sessions. The presence of participants with averages smaller than the fair results in a reduction of the group’s average contribution. the fair (0.51=0.56-0.05). These effects are relatively small but they might be enough to lead groups to collapse, as their baseline contributions are only slightly over the fair (0.56). Importantly, the effect of information might be enough for groups in the Informed treatment to be closer to the tragedy of the commons. This is evidenced by comparing the total contributions in each condition, which indicates that they were smaller when participants were informed (one-sided unequal variances t-test: t9.1 =−2.3, P=0.023 ), though with modest statistical power. Likewise, comparing the means of the two countries groups when playing together suggest that Chinese groups’ total contributions were significantly smaller than from Spanish (one-sided unequal variances paired t-test: t7=2.5, P=0.04 ). These differences are due to some participants having paltry mean contributions in the Informed sessions, as shown by Fig. 4.9. Without information, most participants will likely contribute the fair; with information, however, some of them will free ride. This pattern suggests that Chinese participants might be less willing to contribute when they know they are playing ‘against’ Spanish participants. This hypothesis, however, is unsupported by the results of the Heterogeneous sessions: they indicate no difference between Spanish and Chinese participants with respect to the disclosed information. Naturally, it shows that the relative contributions are smaller when participants have larger targets, a likely result of having a higher toll on their endowment. In this case, the Spanish participants seem to have 66 collective action problems 20 40 Uninformed Informed 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 0.0 2.5 5.0 7.5 0.0 2.5 5.0 7.5 Mean Contribution by Participant China Spain Figure 4.10:Distributions of players’ average contribution in the Heterogeneous sessions. Histogram of players’ mean contributions according to the information provided and the group target in the Heterogeneous sessions. Left (resp. right) panels correspond to groups with a target of 20 (resp. 40). contributed less when they were obliged to make higher contributions than the other group (-0.15), however, we are not able to distinguish this from an experimental artefact. In the Heterogeneous sessions, Spanish participants always started with a larger target, which might have induced them to contribute less, which is not the case of Chinese participants. Thus, it remains an open question whether this effect is valid. Nonetheless, it is remarkable that players from both countries complied adequately with the inequity, even if we consider the negative effect on the Spanish participants’ contributions (1=1.31-0.16-0.15). Curiously, providing information seem to have clustered the contributions around the target in the Heterogeneous sessions, as shown by Fig. 4.10. When players did not know the other group nationality, their average contributions spread almost uniformly over the whole possible range, especially for Spaniards. Suggesting that unknowing the other country nationality might influence the appearance of both free-riding and altruistic behaviour. 4.2.2Discussion The outcomes of Spanish and Chinese participants while playing a collective-risk social dilemma does not seem to be influenced by whether targets are homogeneously or heterogeneously distributed among them. Our analysis indicates that, in general, most participants will contribute around the fair, except by some participants contribut- 4.2 targets and biases:a collective-risk social dilemma between two countries 67 ing less in the Informed sessions. This leads to a reduction in the total contributions of Chinese participants, raising the risk of their groups not meeting the target in the Homogeneous sessions. Notably, this effect is not observed in the Heterogeneous sessions, indicating that, although outcomes are similar, participants might react to information differently in both experimental setups. In general, nonetheless, all participants seem to contribute around or over the fair, even when they have the burden of a larger target. Spaniards’ contribution is smaller than the Chinese’s in this latter case – i.e., LT40 treatment in the Heterogeneous sessions – but not enough to nullify this trend. Moreover, in our setup groups could also have a local threshold, implying that participants are concerned with two groups, one with 12 participants and a subgroup with 6participants, which in turn could increase the likelihood of reaching the target according to some hypotheses [187]. Nevertheless, we observe just a small effect in the other direction for the Spanish participants, i.e., they contribute less when a local target was introduced in the second treatment of the Homogeneous sessions. Seemingly, thus, contributions can be smaller when a local target is present. However, further replications are necessary to confirm whether this result is affected by order effects, as in our setup participants always played with a local target after playing the GT treatment. Either way, the Chinese participants are not affected by the order or local target in the Homogeneous sessions, contributing around the same in both treatments. It seems participants respond well to the targets imposed on them, even when they are larger than the other participating group. This suggests that the application of differentiated responsibilities might be well accepted by rich countries, which should be confirmed by more experiments and work outside the lab. Nonetheless, our results indicate that participants behaviour can differ significantly between heterogeneous and homogeneous sessions, which demonstrates the necessity to investigate what factors might underlie different responses to information. Future work might also be able to unveil whether players from other countries respond differently to information and inequity in targets. One of the difficulties of performing synchronized experiments between two countries, such as the ones presented here, is obtaining large samples for more statistical power. Despite finding statistically significant evidence, our tests at group level rely on small samples, implying caution while interpreting these results. It remains open whether future replications can reproduce our results with more groups. 5 FRAMING & ALTRUISM How selfish so ever man may be supposed, there are evidently some principles in his nature, which interest him in the fortunes of others, and render their happiness necessary to him, though he derives nothing from it, except the pleasure of seeing it. Adam Smith, Theory of Moral Sentiments Seated beggar and his dog, Rembrandt Policymakers, legislators, and public institutions in general must know how people respond to incentives and constraints. For quite some time, at least since Machiavelli, it was believed that humans would always behave selfishly, hence public policy should aim at providing ways to turn human selfishness into social welfare 1 . This justified the widespread uses of material incentives to motivate the supposed homo economicus to act in some specific way. Nevertheless, as we have illustrated in Section 2.2, people have social preferences and disregarding this fact can lead to suboptimal policies [188], or even result in public policy to backfiring [189]. “it is necessary for anyone who organizes a republic and establishes laws in it to take for granted that all men are evil and that they will always act according to the wickedness of their nature whenever they have the opportunity” N. Machiavelli [190] Incentives seldom are orthogonal and additive to people intrinsic responses, indeed, they interact with their moral and psychological motives, possibly increasing their pro-social response synergistically or, on the contrary, undermining it [12]. Ideally, therefore, it is necessary to be aware of the resulting effect of the incentive, or, if not possible, at least observe if it works as intended. Moreover, it also should be taken into account that policies efficacy will also depend on people’s imprecise decision-making process [191]. People behave according to elusive heuristics [191–193] which doubtfully will correspond to the behaviour of a self-interested and rational agent. In fact, humans demonstrate pro-social responses from an early age, which can be undermined by material incentives [4]. Moreover, there is widespread evidence that people contributions and investments are significantly affected by framing effects [191,194]. Thus, to devise effective public policies and sustainable business practices it is imperative to recognize humans’ natural propensity to act altruistically [47] and further identify how people respond in each specific scenario. “it is time to fully embrace what I would call evidence-based economics” Richard Thaler [33] Naturally, applying behavioural experiments are a suitable approach to enhance our collection of people responses in different scenarios. It allows us to grasp how people are expected to behave without the burden of the unintended consequence of an ill-devised policy. In this 1 Samuel Bowles provides a pithy account of the origin of this view in [12]. Interestingly, he shows that even the proponents of the legislating for the selfish man believed that humans had social preferences. 69 70 framing &altruism regard, socially responsible investments and charitable donations are particularly relevant nowadays as global interest in them increases. To uncover people’s responses in these two contemporary investment situations, we have performed two experiments looking in how people’s pro-sociality can be affected by the specifics of i) public goods with donations and ii) impact investing funds – investments whose goal is to generate social and environmental benefits alongside economic returns. In Section 5.1and in Section 5.2we present experiments to uncover peoples’ choices in the first and second cases, respectively. 5.1 framing effects in contributions and donations 71 5.1 framing effects in contributions and donations Framing in multiple goods games and donations to charities, under review. F. Maciel Cardoso, S. Meloni, C. Gracia-Lázaro, A. Antonioni, J. A. Cuesta, Á. Sánchez, & Y. Moreno The number and economic relevance of charities and non-governmental organizations has rapidly grown in the last few decades. For instance, more than 1.5million nonprofits were registered with the US IRS in 2015, contributing around 5.4% to the US GDP [195]; in 2016/17, there were 166,854 voluntary organizations in the UK, employing about 878 000 people [196]. This growth has been fueled by the subsidies of many governments around the world, either by transferring funds directly to organisations or through tax deduction policies to donors[197–204]. At the same time, more than 1billion people give money to charities [205]. In view of this volume of activity, philanthropy and voluntary contributions to charities have aroused the interest of a growing number of researchers in the last decades [206, 207], leading to theoretical models [208], qualitative research [209], and experimental studies on the economics of charity [210], fundraising events [211], different forms of fundraising [212], and the effect of status [213], lead donors [214], rebates [215], subsides [216], and message framing [217] on charitable giving. Secondly, when studying altruistic behaviour in humans, gender differences deserve special attention. Empirical evidence suggests that women give more to charities than men [218]. Socio-cultural and evolutionary theories predict sex-differentiated behaviour [219], although they often disagree on how men and women will behave in specific circumstances. Socio-cultural theory stresses the role of cultural stereotypes [220] whereas evolutionary theory explains sex behavioural differences as adaptations [221]. Particularly, both theories agree on the existence of behavioural differences with respect to cooperation or altruism. Many experiments have been conducted to assess these differences, and in general, women show higher levels of cooperation and altruism than men [222–225], although other studies show that gender does not affect these traits [226,227]. One of the most frequently used frameworks to experimentally address donations to charities is that of public good games (PGG)[46]. The representation of donations to charities through a PGG is far from perfect, but approximate enough to have been considered often in the literature [228–230]. In this context, the research question we address in this work focuses on the effects of framing on both contributions to PGGs and donations to charities 2 . In order to compare the 2See [194] for a recent review on framing in PGG. 72 framing &altruism effectiveness of different fundraising schemes, we have carried out an experiment involving contributing to multiple PGG simultaneously. In this type of experiment, subjects can choose between two or more common pots to allocate their endowments, and the choices made by them are used to assess the effects of different framings [231–234]. In our case, we have compared two distinct methods for raising funds: direct versus indirect donations. To this end, we have devised a specialpurpose PGG with two different treatments: a first setup involving an explicit social fee, or tax (Direct-Donation, henceforth DD), and another one involving an implicit social fee (Indirect-Donation, henceforth ID). As we will see below, our setup allowed us to simultaneously measure two variables: the contributions to public goods and the amounts donated to charity. Regarding those donations, the very existence of a direct self-benefit precludes measuring altruism, and, therefore, we have given the players the chance to contribute to several PGGs, which differed in the fraction of the benefit that goes to charity. Furthermore, the existence of funds with different social taxes enables us to study the pattern of contributions and their corresponding framing effect. Our experiment provides several relevant conclusions concerning how people respond to framings intending to increase contributions with a social impact channeled through charities. We have observed that framing affects the choice of contributions depending on the donation structure: Indirect donations led to greater total contributions than social taxes. Conversely, there was no influence of framing on donations to charity: the fraction of the contributions devoted to charity is not affected by how those donations are presented, i.e., as indirect or as direct donations. Regarding gender influence, we have found that women contribute to public goods and donate to charity more than men. All these findings may have implications of interest for the design of socially responsible investing strategies. 5.1.1Experimental design Figure 5.1shows a schematic representation of the experimental setup. Experiments were conducted on groups of 10 participants. Each group played an iterated PGG with 5funds, which differed in the fraction of profit donated to charity (0%, 5%, 10%, 15%, 20%, respectively). In a standard PGG, participants contribute to a common pot, and the total of the pot is multiplied by the so-called multiplication factor, being subsequently equally distributed among all participants irrespective of their contribution. In every round, subjects were given 100 experimental currency units (hereafter, ECU) which they could distribute among the five funds at will. Arguably, there are two natural approaches to implement donations in a PGG scenario: donations coming from taxes on the contributions or coming from decreases in the profitability. To study the effects 5.1 framing effects in contributions and donations 79 FFC FKP DD ID DD ID 0 5 10 15 Framing Total Donation Direct Donation Indirect Donation A FFC FKP 1 5 10 15 20 1 5 10 15 20 5 10 Round Number Total Donation B Figure 5.3:Total donations to charity in the FC phase. A) Boxplot of the average total donation by subject during the course of the experiment. The lower and upper hinges correspond to the first and third quartiles. The upper (resp. lower) whisker extends from the hinge to the largest (resp. smallest) value no further than 1.5* IQR from the hinge. B) Group averages at each round. The shaded area corresponds to 0.95 bootstrapped confidence interval. Dit =β0+β1IDi+uit (M4) Dit =β0+β1IDi+β2FKPi+β3IDi∗FKPi+uit (M5) Dit =β0+β1IDi+β2FKPi+β3IDi∗FKPi+β4Wi+uit (M6) The analysis confirms that, regarding donations to charity, there is neither difference between treatments nor order effects. Nonetheless, women donate significantly more (i.e., contribute to funds with higher donation rate) than men. 5.1.2.3Distribution of contributions The experiment was designed with five different funds with different social taxes to allow us to study the pattern of contributions and the effects of framing on it. Besides, in the case of a framing effect, being able to extract a pattern in the contributions can help us to investigate the possible drivers behind the differences between the two framings. To study the distribution of contributions in the five different funds, we have carried out regression analyses of the contributions in both FC and KP phases. We performed individual regressions to check whether 80 framing &altruism Dependent variable: Total Donation (4) (5) (6) Indirect Donation 0.198 0.548 0.549 (0.803) (1.002) (0.963) FKP −0.273 −0.010 (1.129) (1.013) Women 3.943∗∗∗ (0.772) Indirect Donation x FKP −0.700 −0.701 (1.601) (1.438) Constant 7.446∗∗∗ 7.583∗∗∗ 5.086∗∗∗ (0.565) (0.660) (0.778) Observations 2,347 2,347 2,347 R20.0004 0.005 0.139 Adjusted R2−0.0001 0.003 0.138 F Statistic 0.546 10.542∗∗ 379.479∗∗∗ Note: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01 Table 5.3:Regression results for the donations to charity. Random-effects (Wallace and Hussain estimator) with cluster robust standard errors at the individual level. Column (4) refers to the model for subjects’ donations with DD as the reference (Equation M4). In (5), two terms have been added to (4): the FKP term taking into account the order, plus an additional term for the interaction between the order and the treatment, being DD × FFC the reference (Equation M5). Column (6) refers to the model (5) plus a Wterm for the gender, being a male subject playing DD × FFC the reference (Equation M6). 5.1 framing effects in contributions and donations 81 the variables’ effects on contributions varied across funds in the two treatments. Equation M7describes the regression for fund f , where the dependent variable Citf corresponds to the amount contributed by subject i , at time t to the fund f . Note that a different regression has been performed for each fund in a given phase. Results of the regressions for the FC (resp., KP) phases are shown in table 5.4(resp., 5.5). Citf =β0+β1IDi+β2FKPi+β3IDi∗FKPi+β4Wi+uit (M7) Table 5.4shows the results for the FC phase, wherein participants could only decide how to distribute their contributions. As shown, participants from different treatments seem to contribute in a similar fashion when funds are considered in isolation. The only significant effect is observed for gender, women being more likely to contribute a larger share to funds with a positive social tax while contributing less to the fund with no social tax. Thus, they end up donating to charity more than men. Table 5.5displays the result of the same regressions for the KP phase, wherein participants can decide the amount they contribute to public goods. Clearly, women also donate to charity more than men in this phase, as they are more likely to choose funds with a higher social tax. There is a higher contribution associated with participants playing the ID treatment in the FFC, nonetheless, this was expected as participants contributed more in total as shown in previous sections. Summarizing, differences in individual funds contributions are a consequence of our previous findings. Specifically, being a woman or playing the ID treatment in order FFC is associated with higher contributions. 5.1.3Discussion In order to explain the observed differences in contributions between the two frames, as well as the observed gender differences, we have studied their possible causes. On the one hand, we have performed regression analyses to evaluate possible differences between treatments with respect to the responses of subjects to the behaviour of the rest of the players in their group, as well as differences in the conditional contribution between genders. The details of these analyses can be found in Section c.1of the Appendix. Regression results indicate that participants do not condition their contribution to other players’ behaviour. There is neither evidence that men or women would react differently to this general trend, nor significant differences between different framings in this respect. A plausible explanation of the observed influence of framing on contributions should lie in how information is presented to the players. 82 framing &altruism Dependent variable: Citf 0 5%10%15%20% ID −3.774 3.521 −3.229 0.047 3.439 (7.048) (3.343) (2.418) (2.339) (3.052) FKP 2.813 −1.925 −3.435 1.632 0.910 (7.122) (1.928) (2.438) (3.641) (3.585) Women −25.784∗∗∗ 2.738 5.441∗∗∗ 5.199∗∗ 12.411∗∗∗ (5.744) (2.545) (1.774) (2.428) (2.358) ID x FKP 1.132 1.236 4.611 −3.437 −3.529 (10.292) (4.389) (3.175) (4.400) (4.677) Constant 58.036∗∗∗ 11.673∗∗∗ 10.405∗∗∗ 10.228∗∗∗ 9.642∗∗∗ (6.121) (2.154) (2.584) (2.020) (2.541) Observations 2,347 2,347 2,347 2,347 2,347 R20.133 0.021 0.047 0.029 0.095 Adjusted R20.131 0.020 0.045 0.027 0.093 F Statistic 358.453∗∗∗ 51.261∗∗∗ 115.645∗∗∗ 70.157∗∗∗ 245.595∗∗∗ Note: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01 Table 5.4:Random Effects regression with cluster robust standard errors at the individual level for the Forced Contribution phase. Each column corresponds to a fund of a determined social tax, namely: 0,5%, 10%, 15%, 20%, from left to right. The reference is a male subject playing DD×FFC. 5.1 framing effects in contributions and donations 83 Dependent variable: Citf 0 5%10%15%20% ID −3.948 0.812 −2.066 −2.292 5.839∗ (5.711) (1.646) (1.776) (1.882) (3.079) FKP 0.017 2.295 0.857 0.846 4.434 (5.480) (1.571) (1.716) (1.764) (3.196) Women −11.060∗∗ 4.103∗∗ 4.643∗∗∗ 5.156∗∗∗ 9.336∗∗∗ (4.718) (1.778) (1.256) (1.377) (2.275) ID x FKP 11.976 5.853∗4.935∗∗ 5.068∗−6.757 (8.265) (3.366) (2.474) (2.658) (4.570) Constant 31.870∗∗∗ 4.616∗∗∗ 5.227∗∗∗ 5.906∗∗∗ 6.479∗∗∗ (5.665) (1.414) (1.350) (1.639) (2.050) Observations 2,363 2,363 2,363 2,363 2,363 R20.057 0.077 0.065 0.063 0.070 Adjusted R20.056 0.076 0.063 0.061 0.069 F Statistic 143.432∗∗∗ 197.424∗∗∗ 162.838∗∗∗ 157.617∗∗∗ 178.595∗∗∗ Note: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01 Table 5.5:Random Effects regression with cluster robust standard errors at the individual level for the Keep in the Pocket phase. Each column corresponds to a fund of a determined social tax, namely: 0,5%, 10%, 15%, 20%, from left to right. 84 framing &altruism In this regard, taxes are only shown to participants playing the DD treatment, being the presence of taxes the main difference between the two treatments. According to this explanation, ID players react negatively to the tax while contributing. Conversely, DD players are not be affected by the reduction in the profitability to the same degree. Furthermore, the fact that the framing effect is observed only in the FKP order suggests that subjects that play first the FC phase are conditioned by this learning effect, being their contributions in the subsequent KP phase independent of the framing. 5.1.3.1Conclusions Summarising our results, by using a setup based on a PGG modified to include a social responsibility factor, we have found that framing will affect fund contributions depending on how the donation procedure is implemented. On the one hand, contributions are higher when the associated social donations are presented as indirect donations than as social taxes. On the other hand, the fraction of the contributions devoted to charity is not affected by the framing effect. This result is not unrelated to the work of Krieg and Samek [234], where they observe that a return of a 20% of the contribution back to the donor increases significantly the contribution level, whereas recognition or sanctions have no effect. We have also found that, on average, women contribute to the public goods and donate to charity more than men, which is observed in some philanthropy contexts [235]. The implications of these findings are crucial for policy-makers in the design of socially responsible investing strategies and fair policies, e.g., when the government or a charity intends to promote socially responsible conducts, or compete successfully for the limited amount of funds available to the different charities. People are not only selfinterested, nonetheless, but their likelihood of acting prosocially can also be influenced by the type of incentive and economic context [12]. In this regard, the results of Corazzini et al. [233] point to the relevance of avoiding miscoordination among donors by making particular options salient. The mechanism we have identified here could then be one option to provide such saliency. 5.2 understanding drivers when investing for impact 85 5.2 understanding drivers when investing for impact Understanding drivers when investing for impact: an experimental study [236]. L. De Amicis, S. Binenti, F. Maciel Cardoso, C. Gracia-Lázaro, A. Sánchez, & Y. Moreno In recent years, impact investing has risen to prominence in a global business environment that is increasingly concerned, and at times even pressured, to take into account social and environmental issues. Impact investing is thus marking a new trend among traditional practitioners, institutions and policymakers worldwide, and the range of impact investment options and opportunities at global level has naturally grown in parallel to the expanding interest in social investment. The Global Impact Investing Network [237] estimates that the sector has grown from $4.3billion in 2011 to $502 billion in 2018 3 and, at the upper end of the market, impact investing is estimated to reach as much as $1trillion in value by 2020 [238]. In light of this new trend, a growing body of research emerged to define the theory and practice of social finance. The GIIN [239] defines impact investments as a form of investment that is “made into companies, organisations, and funds with the intention to generate social and environmental impact alongside a financial return”. According to this interpretation of the term and phenomenon - arguably the most accredited and quoted one - the two defining elements of impact investments are the expectation of financial returns on capital, or at minimum a return of capital, and intentionality, namely the intention of having a positive impact as a direct consequence of a deliberate action. Despite the centrality of expectations and intentionality, current research has mainly focused on impact assessment and measurement frameworks aimed at capturing the environmental and social returns generated by investments ([240], [241]; [242], [243–249] ). While such a focus is critically important to matters of effectiveness, accountability and transparency, it represents a debated and contested field that dominates and largely monopolise research on social investments. Compared to other instances of socially responsible business practices that have been widely investigated through the lens of reputation/brand building and consumption theories ([250], [251], [252]), little research has been conducted on the socio-demographic characteristics and the behavioural drivers pushing investors to choose impact funds over traditional investments. Yet, if we are to make social finance a “standard practice”, it is crucial to look at what might render impact-oriented funds a more appealing investment options and to whom – in this light, this study aims to con3 The estimate is based on the responses provided by 266 leading impact investing organizations from around the world, managing collectively $239 billion. 86 framing &altruism tribute to this research gap through an experiment-based investigation. The value of exploring investors’ behaviour and their decision-making process is two-fold. First, in the context of behavioural economics and game theory, such a focus can add significant value to existing research by shedding light on the nudging factors and determinants influencing the choices of economic actors (i.e., intrinsic value of the research focus). Second, behavioural insights can have implications for normative initiatives or incentive actions aimed at pushing the impact investing trend into the mainstream, such as awareness-raising campaigns, marketing strategies and policy-making (i.e., instrumental value of the research). Within this wider scope of investigation and focus, the present experiment-based research aims to address the following questions: RQ1 What is the effect of previous knowledge about impact investing? Do economic actors invest differently if they are already familiar with the concept of impact investing as opposed to those who have never heard of it? RQ2 How do investors’ preferences change depending on the way different investment instruments are proposed to them? RQ3 How much financial return are investors willing to sacrifice for social impact, considering different risk factors? RQ4 Do external factors affect the behaviour of economic actors (i.e., could incentives from the government change investors’ behaviour)? The experiment consists of a multiple-choice game envisaging different investment scenarios. According to their performance in an effort task at the beginning of the game, participants are given a budget to simulate investment decisions under different incentive circumstances while controlling for different variables, such as prior knowledge about impact investing. The experiment is directed at two different sample groups: non-experts, who are likely to have no prior knowledge on the concept of impact investing, and “experts”, namely professionals working in the impact investing sector. As an incentive to elicit truthful behaviour, and at variance with traditional surveys, participants are economically rewarded according to the earnings they make through their investment decisions. Following the experiment, the data is analysed through logistic regressions. This approach was preferred over percentages as the regression analysis allowed to isolate the effect of each variable. The research design allows to draw a number of conclusions that will be of interest for stakeholders and policy-makers aiming to promote impact investing. The study concludes that people operating in the sector (experts) and female participants tend to favour the impact investing option. Furthermore, the older people are, the more 5.2 understanding drivers when investing for impact 87 Non-experts Experts Female Male Female Male 3-year Bachelor 33 14 1 1 4-year Bachelor 79 45 2 4 5-year Bachelor 59 24 2 3 Lower secondary education 15 10 0 0 Master (1year) 35 20 4 7 Master (2years) 31 15 11 11 Other (non-listed) 20 7 2 0 PhD 7 4 3 8 Post-secondary, non-tertiary ed. 18 20 0 0 Short-cycle, tertiary education 21 18 0 1 Upper secondary education 23 23 1 0 Total 341 200 26 35 Table 5.6:Participants’ level of education . Level of formal education of Non-Experts (two leftmost columns) and Experts (two rightmost columns). attracted to impact investing they appear to be. External factors such as fiscal incentives influence positively, although only marginally, the respondents’ behaviour in choosing Impact Investing Funds (IIF) over Traditional Investing Funds (TIF). No clear correlation has been found between the participants’ educational level and their disposition to invest for impact. Providing additional details or, more effectively, images on the social purpose and impact of the IIF has proved to be critical in substantially increasing the probability of opting for an IIF over a TIF, both for male and female participants. Furthermore, participants were less likely to choose the IIF option when this was associated with higher risk (for both male and female participants). Finally, when considering participants’ prior knowledge on the topic, the difference between control groups was relatively small - yet, it appears that providing participants with key information on social finance (by showing them a video) had a positive impact with normative implications for current incentive structures, awareness campaigns and educational programmes about impact investing. 88 framing &altruism Non-experts Experts Female Male Female Male Argentina 7 1 0 0 Italy 0 0 7 11 Australia 1 0 1 0 Luxembourg 0 0 1 0 Austria 0 0 1 1 Mexico 8 4 0 0 Belgium 1 1 0 0 Netherlands 0 0 2 1 Bolivia 0 1 1 1 Paraguay 1 0 0 0 Brazil 1 0 0 0 Peru 1 1 0 0 Chile 10 1 0 0 Poland 0 0 1 0 Colombia 7 7 0 0 Portugal 2 2 0 0 C. Rica 0 1 0 0 Russia 0 1 0 0 Croatia 1 0 0 1 Serbia 0 0 0 1 Ecuador 0 2 0 0 Spain 282 166 0 2 El Salvador 1 0 0 0 Switzerland 0 0 1 3 France 0 2 2 1 Tunisia 0 0 1 0 France+ 1 0 0 0 U.K. 1 2 7 11 Georgia 1 0 0 0 U.S.A. 2 0 0 0 Greece 0 1 0 1 Uruguay 3 1 0 0 Hungary 0 0 1 0 Venezuela 9 5 0 0 Ireland 1 0 0 1 Zambia 0 1 0 0 Table 5.7:Country of Residence of participants. France+ stands for Overseas France. 5.2 understanding drivers when investing for impact 95 TIF vs IIF Impact Description Risk Factor Intercept 1.05 (0.02)∗∗∗ 1.08 (0.02)∗∗∗ 0.91 (0.02)∗∗∗ Multiple Question −0.03 (0.02)−0.01 (0.02)0.04 (0.02) Delta −0.20 (0.01)∗∗∗ −0.19 (0.01)∗∗∗ −0.16 (0.01)∗∗∗ AIC 3481.80 3270.87 3843.07 BIC 3505.83 3294.91 3867.11 Log likelihood -1736.90 -1631.44 -1917.53 Deviance 558.86 521.04 630.13 Num. obs. 3010 3010 3010 ∗∗∗p<0.001, ∗∗p<0.01, ∗p<0.05 Table 5.11:Framing of multiple questions and fund profitability. Log-odds ratio of coefficients obtained by logistic regression. Each column corresponds to a different regression analysis: TIF vs IIF (Q1and Q2), impact description (Q3and Q4), and risk factor (Q5and Q6). The intercept corresponds to the log-odds ratio which chose the IIF over the TIF (Q1, Q3, Q5). Multiple Question coefficients correspond to the difference in effect when proposing different options (Q2, Q4, Q6) with respect to the intercept (Q1, Q3, Q5, respectively). Delta coefficients account for effect IIFs return (Q2, Q4, Q6), i.e., they refer to the return differences between TIF and IIF. Observations correspond to all participants’ responses to the two-choice questions and their corresponding multiple question (Q1and Q2, Q3and Q4, Q5and Q6). Age also affects responses distinctively in each question, as we discuss further in the next paragraphs. The first column of Table 5.12 shows that: i) Women are more likely to invest in an IIF than men ( p<0.001 ), ii) experts are more likely to invest in an IIF than non-experts ( p<0.001 ), and iii) the willingness to invest in IIF increases with age ( p<0.001 ). On the other hand, the education level does not make a substantial difference in explaining the behaviour of investors. Furthermore, although previous knowledge on impact investing (according to the self-assessment of participants) does not influence the investment decision, the informative video played a positive role: participants who were shown a tutorial video on impact investing displayed a higher tendency to invest in IIF than those who did not watch it (p<0.001). When additional information on the actual impact achieved by the IIF was given to participants (second column of Table 5.12) i) gender differences persist, with women being more likely to invest in IIFs than men ( p<0.001 ), ii) experts are also more likely to invest in IIFs than non-experts ( p<0.001 ). Conversely, neither age nor education has a significant influence on IIF investment choices. Note that, although without additional information on social impact IIF investments increase with age (first column regression), this determinant disappears when additional information is provided (second column). 96 framing &altruism The effects of associating a higher risk with the IIF option (20% chance of not yielding a return with IIF versus a 10% chance with TIF) are shown on the third column of Table 5.12. It is shown that: i) Women are more likely to invest in higher risk IIF options than men ( p<0.001 ), ii) opting for higher risk IIF increases with age ( p<0.001 ). On the other hand, when a higher risk is associated with the IIF, the higher tendency of experts to invest in IIFs vanishes. Regarding tax deductions (fourth column of Table 5.12), surprisingly, a significant effect of tax deductions on the impact investing option was not found, except for experts and older subjects, who display a positive response to tax benefits. It is observed that, when a tax incentive is included in the scenario, experts ( p<0.05 ) and older subjects ( p<0.01 ) show a higher tendency to invest in IIFs. As in previous cases, although prior knowledge on impact investing does not show a significant influence on impact investing choices, participants who watched the informative video showed a higher tendency to invest in IIFs than those who did not see it ( p<0.001 ). This tendency is stronger when a tax deduction is included. Finally, regarding the effect of an additional visual incentive, the fourth column of Table 5.12 shows the logistic regression for the scenario in which additional details on social impact supported by an image were showed to participants. As explained before, the visual aid has a significant positive influence opting for IIFs. In this scenario, gender is the only demographic variable that plays a significant role in the willingness to invest in IIFs - women showed were more likely to opt for IIFs over TIFs ( p<0.01 ). Neither expertise, age, education level, prior knowledge showed a significant influence on investment choices. Although women display a higher probability to opt for IIFs than men in the presence of a visual incentive, it cannot be stated that visual aids affect more women than men, since the difference in its influence is not significant according to logistic regression. 5.2.3Discussion Our results indicate that in most scenarios experts are more likely than non-experts to choose the impact investment option. This does not really come as a surprise: it is likely that experts entered the impact investing field driven by personal principles and moral considerations [259,260], as working in the world of social finance may already reflect personal compromises between a less lucrative career and an ethical professional path[261,262]. Our findings show that older people have a higher tendency to choose impact investment options than younger people. This is somewhat surprising given the current momentum of narratives such as “Millennials Will Bring Impact Investing Mainstream” [263], whereby young generations are expected to shift large capitals towards social 5.2 understanding drivers when investing for impact 97 TIF vs IIF Impact Desc. Risk Factor Tax Ded. Visual Aid Intercept 2.09∗∗∗ 2.87∗∗∗ 1.49∗∗∗ −0.17 2.38∗∗∗ (0.20) (0.22) (0.19) (0.48) (0.64) Male −0.47∗∗∗ −0.50∗∗∗ −0.65∗∗∗ 0.11 −0.78∗∗ (0.09) (0.09) (0.09) (0.23) (0.30) Expert 0.74∗∗∗ 0.65∗∗∗ 0.34 2.23∗1.76 (0.19) (0.20) (0.18) (1.05) (1.09) Age 0.02∗∗∗ 0.01 0.02∗∗∗ 0.04∗∗ 0.01 (0.00) (0.00) (0.00) (0.01) (0.01) H.Ed. −0.11 −0.16 −0.25∗−0.15 −0.06 (0.12) (0.12) (0.11) (0.29) (0.38) P.Ed. 0.05 0.24 0.11 0.20 0.35 (0.14) (0.14) (0.13) (0.36) (0.50) Other 0.31 0.20 0.38 0.30 −0.29 (0.23) (0.24) (0.22) (0.61) (0.70) P.K. 0.15 0.06 0.06 0.22 −0.17 (0.12) (0.12) (0.11) (0.28) (0.39) V. Disp. 0.35∗∗∗ 0.27∗0.27∗∗ 0.98∗∗∗ 0.00 (0.10) (0.10) (0.10) (0.26) (0.34) Delta −0.97∗∗∗ −0.96∗∗∗ −0.71∗∗∗ (0.04) (0.04) (0.04) AIC 3262.16 3084.17 3545.96 551.29 352.44 BIC 3322.26 3144.27 3606.06 590.89 392.04 Log Likelihood -1621.08 -1532.08 -1762.98 -266.64 -167.22 Deviance 3242.16 3064.17 3525.96 533.29 334.44 Num. obs. 3010 3010 3010 602 602 ∗∗∗p<0.001, ∗∗p<0.01, ∗p<0.05 Table 5.12:Demographic variables impact. Each model (column) corresponds to a regression for each framing type. TIF vs IIF considers data from Q1and Q2;Impact Desc., Impact Description from Q3 and Q4;Risk Factor from Q5and Q6;Tax Ded., Tax deduction from Q7;Visual aid from Q8. We consider three three different levels for education: higher education (H. Ed.), postgraduate education (P.Ed.), and other (i.e., non-curricular education besides basic education programs). P.K. is a dummy controlling for previous knowledge about impact investing and V. Disp. (Video displayed) is a dummy indicating if participants have watched the video. Delta coefficients correspond to the return differences between TIF and IIF. Observations correspond to all participants’ responses to questions according to the framing type, columns from left to right: Q1and Q2, Q3and Q4, Q5and Q6, Q7, and Q8. causes, as well as prioritising socially meaningful careers and thus focus on social entrepreneurship [264,265]. Nevertheless, some studies have also shown that senior citizens are more prone to contribute to the common good [266], due to their willingness to leave a positive legacy behind. The explanation for such a result may be that 98 framing &altruism the younger generations are interested in impact investment but do not have enough expertise or do not feel confident enough to take part in it. Indeed, the Financial Times [267] reports that “while 64% of the younger generation Credit Suisse surveyed were interested in impact investing, only 24% had actually invested”. Numbers even decrease when looking at high net worth families. A research from Morgan Stanley [268] shows that only 4% of Next Gen family members consider themselves fully-active participants spending “a great deal” of time engaged in impact investing, although the majority (60%) of Next Gens consider “important” to use their family’s wealth to make a positive social or environmental impact. For almost all the questions, we can observe that women are also more willing to choose an IIF than men, except for the tax reduction question. This is well in line with the abundant literature on philanthropy and charity-giving that shows that women are more likely to engage in altruistic behaviour [235,269]. Even when a risk factor is introduced, more women prefer an IIF compared to male participants despite they are generally considered to exhibit a risk-averse behaviour. The tendency of women to prefer an IIF over a TIF is in line with existing research from the industry. Stephanie Luedke of Citi Investment Management, who works on the front lines of asset allocation, confirmed in a recent interview on Forbes [270] that “90% of women surveyed have indicated that they want to invest at least a portion of their wealth in a manner that aligns with their values”. On the top of that, women are becoming wealthier, thanks to a more gender-equal intergenerational transfer of wealth [271], and are proving to have entered a traditionally "male" environment as capable investors, as showed in a research from Fidelity in which women tended to outperform men in generating a return on their investments [272]. When considering participants’ prior knowledge on the topic, leaving expertise on the side, the difference between control groups is not significant. Yet, the experiment reveals that showing the video had a positive impact in prompting socially oriented decisions, whereby signalling a wider scope for promoting and raising awareness about impact investing. This is confirmed by our logistic regressions and represents one of the most important findings of our research in line with recent studies on the same topic [265]. Public administration bodies and civil society organisations have already started to put efforts in raising awareness about impact investment. Organisations such as Big Society Capital, the social investment “wholesaler” set up in 2012 by David Cameron together with his Big Society agenda, or the Social Impact Agenda promoted by the Portuguese Government are an example of this. International political bodies, such as the European Union, did not adopt a “wait and see” approach; on the contrary, they took significant, active steps forward, such as the creation of 5.2 understanding drivers when investing for impact 99 the Expert Group on Social Entrepreneurship (GECES) in 2011 and the consequent report in 2016 – “Social Enterprises and Social Economy going forward” [273] – advocating for a greater visibility and enhanced understanding of social enterprises and impact investments. This kind of initiatives, however, generated mixed results; more needs to be done not only by coordinating efforts between governments and international institutions but also by encouraging inter-sectorial collaborations between researchers, the private sector and practitioners from the social economy and the social enterprise world, who could work together to gather stronger evidence on the added value of impact investment and better communicate their main results through institutional channels. In this regard, media outlets are currently missing an opportunity, especially in light of the positive general attitude towards the topic in public narratives [265]. Furthermore, impact investing is not currently part of the curriculum of finance degrees and is not part of the formal training of a financier or corporate investor. Top universities are taking new steps in making innovative finance part of the mainstream and are increasingly engaged in the impact investing debate, knowledge-sharing and training. For instance, the Said Business School at the University of Oxford has recently launched a programme entitled “Oxford Impact Investing Programme: Build your investment skills to deliver maximum social return”, directed at professionals and businesses that aim to enter the field - this integrates the work already undertook by the Skoll Centre for Social Entrepreneurship. In the same way, the Cambridge Institute for Sustainability Leadership (CISL) greatly focuses on sustainable business and leadership. Yet, these standarn university degrees hardly cover impact investing. As a result, whilst universities are increasingly treating topics related to management and innovation for social good, there is still a long way to go in shifting the way we approach mainstream financial training and education, which could be a great starting point to radically change mainstream finance. Another reflection point is about tax incentives, usually seen as a strong market builder. In our experiment, the tax incentive is the only case in which gender does not play a significant role, and both men and women do not see it as an incentive. This was a somewhat surprising, key finding of our research. As a matter of fact, despite what academic evidence suggests and our experiment confirms, public bodies still put a great emphasis on the tax benefits of giving. The UK Government, for instance, has introduced the Social Investment Tax Relief (SITR) scheme in 2014 - yet, the results have not been as positive as expected. In 2016-17,25 social enterprises received new investments through the SITR scheme and £1.8million of funds were raised. Since SITR was launched in 2014-15,50 social enterprises raised funds of £5.1million through the scheme [274]. These figures are far from the 300,000 social enterprises and charities that could potentially benefit 100 framing &altruism from SITR, according to Big Society Capital [275]. What is causing such a big difference? In a recent call for evidence launched by the British Government, organisations advocated for several changes suggesting that such incentives were not fit for purpose [276]. In this regard, our study confirms that tax incentives are not a game changer for people who are not experts in the field. One may wonder whether the problem lies in the design of incentive schemes or in the fact that tax incentives themselves are simply not a major determinant of investors’ decisions. Other countries have launched similar tax incentive schemes in the past (i.e. France) and others (i.e., Italy) have just followed. In a few years from now, it would be interesting to see the impact of these recently implemented incentives and run further research to understand whether fiscal incentives can still be considered as a main driver for investors’ behaviour or are just a nice add-on impacting the decision of ’only’ a few. The experiment also brought about the lingering scepticism about impact investing. Indeed, impact investing is still perceived by some as a suspicious hybrid where money-driven actors, philanthropists and practitioners (i.e., social entrepreneurs) are culturally polarised and still struggle to speak the same language [265]. By way of example, one of the participants - and more specifically a participant from the expert pool – reported feeling “almost angry” at the built-in reward mechanism of the game. He contested not feeling included in the scope of the experiment, which according to the participant implicitly assumed that people can only be incentivised by money; consequently, in this view, the experiment was meant for profit-oriented “venture capitalists” only. While the design of the game was merely aimed at resembling real-life circumstances, we did not predict that offering a reward could have triggered negative reactions. In the same way, another expert participant never claimed the prize, thus showing his ’pure’ willingness to engage in the debate and lack of responsiveness to monetary incentives. 5.2.3.1Conclusions Impact investing aims to generate social and environmental impact alongside a financial return. Here, we have run an experiment with 602 participants to understand what ’makes’ impact investors and what are the drivers for their decisions. We apply logistic regression analysis on the acquired data-set. One of the main weaknesses of the study is the sample limitation for experts. However, we must note that the process of finding experts and get them to run the experiment requires considerable resources. There is not such a thing like a pre-defined available data-set for this, and therefore having access to experts and ensuring their participation to the experiment is a challenge in itself, also due to their time limitation. 5.2 understanding drivers when investing for impact 101 The main contribution of this work is the domain insight: our study shows that participants are generally favourable to invest in IIF, especially if they are women, older people, or individuals who were already familiar with the impact investing field (i.e., “experts”). With reference to this last point, while prior experience in the field has an impact on choices ( RQ1 ), there was no significant difference between non-experts who reported some or no previous knowledge on impact investing. This might lead to two competing explanations: i) non-experts who declared to have some knowledge on the field knew about it only vaguely; ii) simply knowing about impact investing is not enough, and prior experience rather than mere knowledge is a more significant determinant of choices. Surprisingly, external incentives such as tax breaks do not appear to be a game-changer ( RQ4 ), and future research might determine when and why they might affect investors’ decisions. On the other hand, when participants are informed of the risks attached to their investment, the likelihood to invest in an IIF decreases ( RQ3 ), but it increases when more information about the impact of their investment is made available ( RQ2 ). Particularly, we have seen that visual aids further increase the investors’ willingness to choose an IIF across all categories analysed in this work. We note that additional efforts should be made in raising awareness about impact investment, especially by policymakers and media outlets. Inter-sectorial collaboration between the public, private and third sector and academia (quadruple helix) should be encouraged, as well as the introduction of impact investing in the curriculum in financial training and education. Future researches could benefit from a broader dataset. Tax incentives deserve special attention and researchers could focus on those countries that have already designed and implemented policies on this topic. An interesting twist to the research could be investigating how behaviour changes if the choice of the participants is made public, as an interest in reputation-building and positive self-branding may significantly drive people’s choices. 6 TRADING IN COMPLEX NETWORKS Market at Gisors, Rue Cappeville, Camille Pissarro Whoever offers to another a bargain of any kind, proposes to do this. Give me that which I want, and you shall have this which you want, is the meaning of every such offer; and it is in this manner that we obtain from one another the far greater part of those good offices which we stand in need of. Adam Smith, The Wealth of Nations Up until now, we have dealt with scenarios wherein the manifestation of humans’ pro-social tendencies provides the most efficient outcomes for the group. Nevertheless, in some situations, people or companies coalescing can have harmful effects to social welfare, such as in the case of oligopolies and cartels. They are detrimental by going against one important feature of markets: free competition. In an ideal market, the existence of many buyers and sellers would guarantee long-run efficiency in a barrier-free environment. As pointed by Adam Smith, competition would make market prices converge to their natural level and also push the economic system to higher levels of productivity and innovations [29]. Thus, without requiring a Leviathan [134], decentralized trade would work for the social welfare of the majority of people [277]. “buyers and sellers are in such free intercourse with each other that the prices of the same goods tend to equality easily and quickly.” A. A. Cournot [278] Consequently, concerning market interactions, competition can be seen as beneficial to the social good as cooperation is in social dilemmas. Nonetheless, in the real world, factors such as information asymmetries and cumulative advantage can lead to market inefficiency [279]. Specifically, structures centralizing market power would undermine competition, leading to monopolies and monopsonies determining prices [280]. Therefore, it is in the public interest to identify such structures in order to ensure free competition endures. In this regard, most markets show an underlying network structure which has to be taken into account if we are to understand market outcomes [55,281,282]. Indeed, economic interactions are influenced by geographic proximity and individuals’ relationships [283]. Moreover, global supply networks in agriculture, manufacturing, and services are a defining feature of the modern world, and trading outcomes are affected by all sorts of middlemen connecting producers to buyers [284]. Accordingly, the efficiency and the distribution of surpluses across different parts of these networks depend on the decisions of their intermediaries. In particular, their position can make them extract a large fraction of the trade surplus, and they can be positioned in such a way as to make trade inefficient [72]. 103 104 trading in complex networks Consequently, it is crucial to identify the principles governing intermediaries behaviour, especially if they decide simultaneously [279]. Furthermore, there is a non-trivial interplay between decisions and economic agents’ links if the underlying network exhibits a complex topology [62], such is common in real systems [55,285]. Thus, to improve our insights about these type of markets, in this Chapter, we present results of price formation experiments performed with human subjects located in large complex networks. Moreover, the observed behaviour leads us to create an agent-based model yielding macroscopic patterns consistent with the experimental findings. In sum, the results presented in this Chapter show that network topology is a chief determinant of pricing and efficiency. 6.1 effect of network topology and node centrality on trading 111 Not in Selected Path In Selected Path R26 SW26 R26 SW26 -2 0 2 Mean Change in Price SW26 R26 N Y N Y 0.00 0.25 0.50 P A B Increased Decreased Figure 6.4:Being or not in the cheapest path determines the intermediaries price increases. A: Mean changes in the posted price conditioned to have been (right) or not (left) in the selected cheapest path in the previous round for the random networks of 26 nodes (R26), and for the small-world network of 26 nodes (SW26). B: Probability to increase (blue) and to decrease (pink) the posted price conditioned to have been (Y) or not (N) in the selected cheapest path, for each one of the studied networks. The error bars represent the 95 % C.I. An extension of these results including the 50-nodes Random Network is displayed in Appendix Fig. b.2. measures, which explains why – in a situation where prices are largely insensitive to network location – profits will be correlated with sd∞(v) . The robustness of these results against the size and connectivity of the network is discussed in the Appendix Section b.1. So far, we have seen that node centrality does not influence earnings when we equally consider all the paths from S to D to compute it, but it does when we consider only the shortest paths. This fact indicates that the weight given to paths length is important to study the capacity of the nodes to extract surpluses. In order to verify this hypothesis, Fig. 6.3G shows the coefficient of determination R2 of the regression of intermediaries payoffs on sdα as a function of α . The best fit is obtained for α∼12 , which indicates that longer paths should have significantly smaller weight than shorter ones. As the number of paths grows exponentially with network size, SD-betweenness seems to be a feasible and good descriptor of participants’ earnings. 6.1.3Behavioural rules We have noted that participants’ behaviour is not determined by network position: criticality and classical measures of centrality are not good predictors of the prices posted by intermediaries. Nonetheless, results show differences in the prices posted by traders across different networks. Even if these networks might seem relatively small and 112 trading in complex networks 50 100 150 200 R26 SW26 Network Cost 10 20 R26 SW26 Network Mean Price in Cheapest Path Figure 6.5:Numerical results of the model executed over the networks, source and destination from the experiments. Results shown are for 100 executions with 15 rounds for each network and source-destination pair, excluding the first round. Initial prices are bootstrapped from the experimental values. Values of σ and ρ are fixed and correspond to mean values of the experiment, respectively, 2.60 and 1.2. similar, they are not. The environment (defined as the set of all the information that the individuals need to factor in their decisions) is very complex: there are many different paths passing through most of the traders, they need to take into account their price as well as those of other players, etc. It is thus reasonable to assume that the traders confronting such a complex and dynamic environment use rules of thumb, which on the other hand, should not depend on the network. In what follows, we develop a model that accounts for individual behaviour and for the differences observed experimentally. Together with the network information, the other information shown to subjects is whether they were on the selected trading path. Fig. 6.4A shows, for each one of the networks considered, the mean change in price for the cases when the participant was or was not along the cheapest path in the previous round. In the same way, Fig. 6.4B shows the probabilities to increase and to decrease the posted price conditioned to have been (Y) or not (N) in the cheapest path. Players appear to follow a simple rule, namely, to increase their price if they were on the cheapest path in the previous round and to decrease it otherwise. Furthermore, the expected values shown in Fig. 6.4A point out that successful intermediaries keep increasing their prices and therefore, without sufficient competition, costs and prices would always grow. We now build a simple agent based model (ABM) [305], as described below: i) If node u belongs to a cheapest path at time t , it will change its posted price on time t+1 by σ; ii) If node u does not belong to a cheapest path at time t, it will change its posted price on time t+1 by −ρ; 6.1 effect of network topology and node centrality on trading 113 50 100 R SW R SW 0 50 100 Network Cost 50 100 R SW R SW 0 5 10 15 20 25 Network Mean Price in Cheapest Path Figure 6.6:Numerical results of the model for networks with 50 and 100 nodes. Results shown are for 100 executions with 15 rounds for each network and source-destination pair, excluding the first round. Initial prices are bootstrapped from the experimental values. Values of σ and ρ are fixed and correspond to mean values of the experiment, respectively, 2.60 and 1.2 . For similar analyses with random initial prices, see Appendix Fig. b.6. iii) The minimum price a node can post is 0. network efficiency price price in CP cost length R26 0.87 14.71 11.87 75.68 7.62 SW 26 0.66 15.14 12.56 94.32 8.97 Table 6.2:Numerical results in experimental networks. Efficiency (fraction of rounds in which the cheapest path cost was equal to or less than the threshold), and mean values of the price, price in the cheapest path, cost of the cheapest path, and cheapest path length. Results obtained from numerical simulations with each one of the two studied networks with their corresponding source and destinations. To validate this model we executed it by bootstrapping the initial prices, the value of changes if on the cheapest path ( σ ) and the value of changes if not ( ρ ). The results, shown in Fig. 6.5, indicate that costs from simulations (resp. efficiency) are higher (resp. lower) in smallworld networks than in random networks (t(9659.3)=68.33, p<0.001 ), in agreement with our experimental results. Costs reached relatively high values in some rounds, as the model does not incorporate participants direct response to the maximum cost threshold. Table 6.2 also confirms that topological differences between the networks are driving the differences in cost. Once we have shown that the model captures very well the experimental observations, we verify if the same phenomena are observed in larger networks. Results for networks of size 50 and 100, shown in Fig. 6.6and Table 6.3, are also consistent with the experimental 114 trading in complex networks data, confirming that the network topology has a significant effect on trading outcomes: small-worlds lead to higher costs and lower efficiency. A similar analysis with random initial prices, thus unlinking numerical results from those obtained from the experiments, can be found in Appendix section b.3.3and Fig. b.6. Results in Fig. b.6are compatible with those shown in Fig. 6.6, providing more evidence about the effects of the network structure on prices and costs. network efficiency price price in CP cost length R50 0.98 13.12 7.03 44.76 7.68 SW 50 0.91 14.32 8.28 77.44 10.74 R100 0.97 12.65 5.53 46.50 10.05 SW 100 0.82 13.20 6.56 88.56 15.41 Table 6.3:Numerical results for larger networks. Efficiency (fraction of rounds in which the cheapest path cost was equal to or less than the threshold), and mean values of the price, price in the cheapest path, cost of the cheapest path, and cheapest path length. Results obtained from numerical simulations with random networks with 50 and 100 nodes (R 50, R 100) for the small-world network with 50 and 100 nodes (R50, R 100). 6.1.4Topological properties behind the differences in cost Finally, we go one step further in order to explain what lies behind the differences found in costs. One possible theoretical hypothesis could be that costs depend on competition between paths. In our setup, this would be equivalent to assume that costs should decrease with the number of possible ways to reach the destination, i.e., the number of independent (sets of) paths from S to D. Specifically, we expect competition to be proportional to the number M of node-disjoint paths [306], as it captures the possible number of simultaneous independent trades (see Appendix Section b.3.1for a deeper discussion on this subject). According to this hypothesis, the larger the value of M , the lower the cost. Another possible explanation for the dependency of costs with the networks could be the structural differences between the latter. It is well known that clustering coefficients and average path lengths differ for the SW and the random networks considered in our experiments ( p∈ {0.1,1} [59]), and therefore the observed differences in cost could be tied to variations in those properties. In order to verify the previous hypotheses, we executed a version of the model without the maximum cost threshold. With this setup, we can study long-term effects after a sufficiently large number of rounds and uncover the cost tendency. In this regime, we cannot analyse network efficiency, however, networks yielding higher cost should be 6.2 conclusions 115 more inefficient. Note that the proposed model allows extrapolating the observed behaviour to larger networks with a large range of values of M . Then, we can generalize the observed experimental results to larger networks, which allow us to find the (theoretically conjectured) influence of M on prices. We ran the algorithm for 104 rounds and then we considered the final cost of the trade for each configuration. Results for networks of size 26,50 and 1000 nodes are shown in Figures 6.7A, 6.7B, and 6.7C, respectively. Simulations of trading dynamics on the aforementioned networks indicate that the number of node-disjoint paths ( M ) between S and D is the best indicator of final cost. Fig. 6.7D shows that as M grows, the costs are reduced so drastically that they go to 0for M>3 . Moreover, the numerical results also reveal that for networks with the same value of M , the cost grows with the average path length. Indeed, this dependency explains why costs on small-world networks tend to be larger: these networks have a larger average path-length. To show that this finding is not a consequence of differences in the length of the cheapest paths, Fig. b.4of the Appendix displays, for the same simulations, the costs of the cheapest path normalized by the number of nodes on it versus the average path length of the network. It can be seen that the mean price of nodes in the cheapest path also correlates with the average path length. Interestingly, even though in this regime the difference in the clustering is larger than the difference in average path length, the former is not as good as an indicator of costs ( R2=0.57 vs R2=0.79 , see Section b.3.2, Table b.2, and Fig. b.5in the Appendix). In summary, these results provide two stylized facts that may guide future inquiries in this line, namely, trading costs will be null in setups with a relatively large number of node-disjoint paths and costs should be larger in networks with larger average path length. 6.2 conclusions Our experimental results indicate that the trading network has a powerful effect on both the pricing behaviour of intermediaries and the overall efficiency of the system, random networks being more efficient and showing significantly lower prices than small-world networks. However, within a network, prices are relatively insensitive to node location, but intermediaries with greater betweenness make larger profits. Informed by the experimental results, we introduced an ABM of pricing behaviour to understand traders’ pricing. The key input of the model is the experimental observation that intermediaries raise prices when they lie on the cheapest path and lower their prices otherwise. The model successfully reproduced qualitatively the experimental results and allowed us to extrapolate and anticipate outcomes of pricing and efficiency to scenarios involving larger networks and longer timescales. Important enough, the model also enabled 116 trading in complex networks R SW 123 A 0 3 6 9 0 2 4 6 Average Path Length Cost B 0 5 10 15 20 25 0.0 2.5 5.0 7.5 10.0 Average Path Length Cost C 0 5 10 15 0 5 10 15 Average Path Length Cost D 0 2 4 6 8 12345 M Cost Figure 6.7:Numerical results of the model. A,B,C : Average final cost (in 104 ) of the cheapest path after a period of 104 rounds as a function of the average path length of the network. Different panels correspond to different network sizes: 26 ( A ), 50 ( B ), and 1000 ( C ) nodes; colours correspond to different network models: random (blue) and small-world (magenta); and different shapes correspond to different values of the number M of disjoint paths. For each configuration, there were generated 10000 networks of size 26,50, and 1000, according to the Watts-Strogatz algorithm [59] with p=0.1,1 and average degree from 2to 10. The initial cost was set to 0and the increment/decrement ratio was fixed to the experimental value ( σ/ρ=2.4 ). Results for M>5 are not shown as costs converge fast to 0. D: Mean value of the cost of the cheapest path versus Mfor the same networks. 6.2 conclusions 117 the discovery of what are the key determinants of cost, namely, the number of node-disjoint paths from source to destination and the network average path length. Ultimately, this explained the differences in our experimental results: in a small-world network, the average path length tends to be larger and this leads to higher costs and lower efficiency of trading in these networks as compared to random networks. Overall, our work reveals that the topology of trading networks is key to determine their efficiency and cost. It would be interesting to further test our conclusions using real data on trading, in particular, the finding that the availability of node-disjoint paths takes trading costs down. On the other hand, our insights may be useful for the design of competition-improved networks for goods currently overpriced due to intermediation. Further research on the role of information provided to intermediaries and on other network topologies will be also relevant to address these issues. 7 MODELLING THE EVOLUTION OF COOPERATION In all these scenes of animal life which passed before my eyes, I saw Mutual Aid and Mutual Support carried on to an extent which made me suspect in it a feature of the greatest importance for the maintenance of life, the preservation of each species, and its further evolution. Mutual Aid: A Factor of Evolution, Kropotkin Figure with Drawers for a Four-part Screen, Salvador Dali The results presented in the last chapters have shown how experiments can be used to obtain knowledge of human behaviour. A next step in the scientific dynamics is formulating new theories that can be tested by new experiments [30], or looking at the implications that the observed behaviour can have in systems that cannot be reproduced in the laboratory, such as we have done in Section 6.1.3. This especially important when studying social systems, given that humans usually live in large groups [2,3], a condition that is unfeasible of being reproduced in a controlled experiment. Even though large systems can be replicated to some extent [17], some scenarios are just impossible, such as reproducing the evolutionary process of humans or other animals. In these situations, computer simulations are probably researchers’ best tool [307], capturing emergent phenomena in situations that closed-form solutions cannot be obtained [115,308]. “This is the essence of intuitive heuristics: when faced with a difficult question, we often answer an easier one instead, usually without noticing the substitution.” Daniel Kahneman, [309] Agent-based models (ABM) are especially important in this regard, [305], belonging to a third way of doing science according to Robert Axelrod, having strong assumptions as deduction, but coming to conclusions of the simulated data via induction [307]. Simulations of ABM allow exploring answers to complex questions, such as one underlying this thesis: how the cooperative behaviour observed in humans have originated? This question is not free from controversies, as we discuss in Sections 2.4.4and 8.1. We attempt to contribute to this discussion in this Chapter by using evolutionary game theory, but without the hard assumptions of pure strategies. Instead, we rely on heuristics, which correspond to the method used by humans when making decisions [192]. Moreover, we use evolutionary algorithms [310] to model the dynamics of strategies selection and, thus, uncover the emerging heuristics. As we present in the next section, our findings resulted to be very insightful, shedding some light in how the evolutionary process might differ between humans and other non-human animals. 119 120 modelling the evolution of cooperation 7.1 dynamics of heuristics selection for cooperative behaviour Dynamics of heuristics selection for cooperative behaviour, under review. F. Maciel Cardoso, C. Gracia-Lázaro, & Y. Moreno Game theory constitutes a powerful framework for the mathematical study of social dilemmas [19,20]. Within this framework, the most representative and widely used game to model cooperation, the Prisoner’s Dilemma, has become a paradigm for modelling the evolution of cooperative behaviour [23]. The Prisoner’s Dilemma mimics the worst possible scenario for cooperation in which selfishness always provides a higher individual benefit than cooperative behaviour. Initial predictions indicated the social optimum would not be reachable by rational selfish individuals if the temptation for defecting ( T ) exceeded the reward for cooperating R . Nonetheless, cooperation is pervasive in human and animal societies [311–313], and a vast literature has demonstrated how cooperation can thrive in the presence of an appropriate evolutionary process [24,26,91,111,113,115,314–316]. The possible situations where cooperation might flourish are endless, and we are just beginning to uncover the ingredients behind the complexity observed in real systems [40,155]. Consequently, theoretical studies usually focus on simplifications, such as individuals behaving according to fixed pure strategies [111,115] or some arbitrary set of them [317,318]. Yet, the reasoning and motivations of humans are more sophisticated and complex than pure strategies and decisions are usually taken factoring in many ingredients, weighting them differently [192]. In other words, generally speaking, the selection of strategies takes place in complex systems wherein imprecise behaviour and the environment are inputs of each other in a perpetual feedback loop [319]. In this line, behavioural economics has shown that humans respond in unexpected ways [33,193] and often seem to possess hardwired heuristics while acting in experimental situations [320,321]. Experiments have also shown that humans automatic responses are modelled by experiences from daily-life, building heuristics or intuitions which tend to favour cooperation [150,154]. Therefore, it is plausible that cooperative societies are sustained by existent heuristics, maintained by norms [2,101] or biological factors [82,155,320], that have resulted from a selection dynamics. It is thus imperative to understand how such possible heuristics have evolved, which will allow explaining the ingrained mechanisms behind the behaviour observed in living beings. Here, we investigate the evolution of cooperative strategies through an agent-based model of heuristics selection inspired by evolutionary 7.1 dynamics of heuristics selection for cooperative behaviour 127 0 0.0001 0.05 1 LTT RRN 0 0.25 0.5 0 0.25 0.5 0 0.25 0.5 0 0.25 0.5 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 Fraction of cooperative actions Generation (105) Figure 7.3:Fraction of cooperative actions at the end of each generation . Columns correspond to different mutation values (0,0.0001,0.05, 1) and horizontal panels to different networks (LTT, RRN). Agents have memory m=1 and 100 realizations are performed for each mutation value and network. The colours of the lines correspond to the average of the last 1000 generations. gies to prevail and defection tends to increase, however, a sufficiently small mutation probability will guarantee that the system evolves to a cooperative equilibrium. 7.1.2.1Other payoff values To ensure that our results are robust with respect to differences in the payoff values, we ran simulations for different values of the temptation parameter T . To make our results comparable to previous work, we used the one-dimensional parametrization of payoffs used by Nowak et. al [111]. In this version, R=1 , P=e , S=0 , and T varies from 1to 2, with e being a value close to zero. As we consider normalized versions, the payoff here is defined by T=T0/hki;R=1/ hki;P=0.01/ hki;S=0 , with T0 varying from 1 to 2. Results for memory 0and 1are shown in Fig. 7.4. The results show that without memory, cooperation is only attainable when T0=1 and low mutation. However, when agents have memory of their last interaction, cooperation endures even when the temptation to defect is around 2. 7.1.2.2Heuristics and Strategies In this section, we focus on the composition of the populations in the different regimes. It is not straightforward to evaluate how genes and 128 modelling the evolution of cooperation 0 1 1.00 1.25 1.50 1.75 2.00 pm T' 0.00 0.25 0.50 0.75 1.00 Average Cooperation 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 Figure 7.4:Average cooperation at the stationary state . The left panel shows results for m=0 and the right panel for m=1 .100 simulations were done for each pm and T0 combination. Colour coding corresponds to the average over all realizations and varies from blue (1) to yellow (0). variables interact, hence, it is hard to determine if agents are going to cooperate or not in a specific situation. A first step is to investigate what are the gene values in cooperative and non-cooperative equilibria. Fig. 7.5show the distributions of genes for two mutation values: pmut =0.05 and pmut =1 , wherein evolution leads to mostly cooperation and to mostly defection, respectively. Simulations in both LTT and RRN networks yielded similar distributions, indicating the presence of a common evolutionary pattern. When the majority of the population cooperates ( pmut =0.05 ), β0 , C1 , and R1 have a clear right-modality with most of these values being higher than 0. Conversely, D1 is left-modal with a clear peak at extreme negative values, while P1 shows a softer trend towards negative values. This implies that when cooperation thrives, agents have a baseline cooperative response and tend to reciprocate cooperation both directly and indirectly. On the other hand, the agents punish defectors rigorously and have a mild negative response to other agents’ payoff, probably as a means to punish defectors, as only defectors can attain the highest payoffs. Interestingly, the distributions of β0 indicate that the emerging strategies are willing to cooperate even in a one-shot game with an unknown player as show in Fig. 7.7, albeit this is not the expected behaviour for m=0 . In the other extreme, for pmut =1 , defection prevails, and genes values indicate the underpinnings of this trend. All distributions are right-skewed, with β0 and D1 having a noticeable peak at the lowest possible values. Thus, when mutations are too frequent agents are much more likely to exploit and punish, leading defection to be the default strategy. Too much drift will make it impossible for cooperative heuristics to be selected, and they will vanish in the population. 7.1 dynamics of heuristics selection for cooperative behaviour 129 Figure 7.5:Distribution of genes’ expressed values. Densities of genes values for simulations on LTT and RRN graphs for m=1 . Top panels show distributions for pmut =0.05 and bottom panels for pmut =1 . The vertical dashed line indicates separate regions wherein the marginal probability to cooperate would be smaller (negative gene values) and greater (positive gene value) than 0.5. These last results provide a picture of the genotype space. However, there is still the need to identify which strategies have emerged. When studying evolutionary games, it is always challenging to bridge the gap between the genotype and phenotype spaces [323]. In our model, the profile of agents’ actions would correspond to observable phenotypes, yet it is not straightforward to specify a method for heuristics classification. An unsupervised procedure would fall into the problem of how to identify the groups encountered, i.e., how to determine to which known strategies they correspond. Therefore, here we adopted an approach that consisted of classifying agents by looking at what would be their responses to the most basic strategies: a pure defector and a pure cooperator. Namely, we looked at whether agents were likely to cooperate or defect with agents having a history corresponding to each of the two pure strategies. For instance, a full defector v would always have defected with u ( C1 v,u=0 , D1 v,u=1 ), with its other neighbours ( R1 v,u=0 ), and would have an expected payoff ( π1 v ) corresponding to these actions. Table 7.2illustrates the variables contained in the memory of agent u with respect to a player v , corresponding to the two pure strategies for m=1 . All the values are given straightforwardly, expect for π1 v . Payoffs values are more complicated, as they depend on the players with whom they are playing with, which we cannot define a priori. We 130 modelling the evolution of cooperation Pure Cooperator Pure Defector C1 v,u1 0 R1 v,u1 0 π1 vhπCi hπDi D1 v,u0 1 Table 7.2:Pure strategies memory. Past history of the two basic strategies according to what would have been played by them for m=1. Pure Cooperator Pure Defector FC C C FD D D CC C D GCC CCD - D Bully D C Random - - Table 7.3:Classification of heuristics according to their responses to the two pure strategies: pure defector and pure cooperator. We consider that agents cooperate ( C ) or defect ( D ) if their probability to cooperate is greater than (1−σ)or smaller than σ, respectively. decided to use the average payoff of individuals which cooperated and defected with all their neighbours for the pure cooperator and pure defector, respectively. Therefore, hπCi=hπt ii∀i∈R1,∀t∈[1,100] and hπDi=hπt ii∀i∈R0,∀t∈[1,100] , wherein R1 (resp. R0 ) corresponds to the set of agents which cooperated with all (resp. none) of their neighbours in the last time step. We then, use the threshold σ to divide the plane (ρC,ρD) . Namely, we designate as cooperation when ρ>(1−σ) , defection as ρ<σ , and random (-) when σ≤ρ≤(1−σ) . This process results in the proposed classification is shown in Table 7.3. We considered strategies analogous to known ones, namely: Full Cooperator (FC), cooperates with both pure cooperators and pure defectors; Full Defector (FC), defects with both; Conditional Cooperator(CC), reciprocates cooperation and defects otherwise; Generous Conditional Cooperator(GCC), reciprocates cooperation and can cooperate randomly with defectors; Conditional Defector(CD), cooperates randomly with cooperators and always defects with defectors; Bully, defects with cooperators, but cooperates with defectors; Random, behave randomly with both pure strategies. We labelled agents that could not be classified by this process as Undefined. 7.1 dynamics of heuristics selection for cooperative behaviour 131 In Fig. 7.6, we show the frequencies of each strategy from simulations of the heuristics selection dynamics. Top panels ( A ) show strategies for a lattice and bottom panels ( B ) for RRN networks. Results in both networks types are very consistent: when the mutation is low ( pmut =0.05 ), most of the agents tend to be cooperators or conditional cooperators (mean fraction is 0.9with a standard deviation of 0.07): CC constitutes most of the strategies, followed by a small fraction of GCC and FC players. In contrast, when mutation is high ( pmut =1 ), FD and CD constitute the majority (mean=0.66, sd=0.038) of agents. However, a minority of CC players can persist (mean=0.17, sd=0.022), which explains the existence of a small fraction of cooperative actions even in this regime. 7.1.2.3Exploring kin discrimination: a first extension. It is known that cooperative behaviour can emerge and be sustained by factors that do not depend on players history of decisions. Namely, genetic relatedness or kinship plays a key role in the evolution of cooperation in nature [79,82,83,89]. Kin selection is pervasive [311, 312], despite controversies over its role in particular phenomena [84, 107,108,110,330,331]. Indeed, these disagreements indicate the need to investigate the role played by genetic relatedness in each specific scenario [84]. Therefore, to address this question, we take such mechanisms into account in the evolutionary dynamics of heuristics selection. Namely, we have extended the previous analysis and considered that agents could evaluate an additional variable that accounts whom they are interacting with, specifically, genetic proximity, which is one main mechanism ensuring interactions occur among related individuals [79]. We added to the agents’ chromosome a gene K to account for genetic relatedness with the interacting agent. Operationally, we consider that this kinship relation is given by the Jaccard index of pairs of agents’ chromosomes. Note that we are not specifying a method for kin selection, but allowing the heuristics to take into consideration agents similarity when deciding to cooperate or not. Enabling, thus, an estimation of the relevance of genetic relatedness by evaluating the weight organically given to the heuristics’ new gene. Results of simulations on a lattice are presented in Figure 7.8. Figure 7.8A shows the fraction of cooperation at the steady-state both for our previous model (Non-Kin) and for the extended model (Kin). The evolution leads to similar scenarios in both cases, indicating that the presence of the ( K ) gene did not enhance nor undermine cooperation significantly, though there is one modest exception. For heuristics without memory ( m=0 ) and low mutation, there is a modest increase in the level of cooperation. At variance with the model in a lattice, when there is no mutation, the fraction of cooperative actions can be different from zero in an RRN network, as shown in Fig. 7.9A. This 132 modelling the evolution of cooperation A B Figure 7.6:Emerging Strategies. Frequency of each strategy in executions in LTT (top panels A ) and RRN (bottom panel B ) networks for pmut =0.05 , σ=0.3 and m=1 . Each red dot correspond to the fraction of the strategy in a simulation and the histogram of fractions for each strategy is shown vertically, with darkest colours representing a higher number of occurrences. 7.2 conclusions 133 LTT RRN 0.05 1 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 0 10000 20000 30000 40000 0 10000 20000 30000 40000 ρoneshot count Figure 7.7:Cooperation probability in one-shot games . Distributions are calculated over agents of the final generation for m=1 in a lattice (left panel) and in random regular networks (right panel). Probability is calculated considering that agents do not have access to other participants information, thus, only β0 is used in the sigmoid. Top panels show distributions for pmut =0.05 and bottom panels for pmut =1. demonstrates how important the kin identification mechanism can be in an adequate environment. Despite the negligible differences in outcomes, there is a substantial effect on agents’ chromosomes. Fig. 7.8B (resp. 7.9B) shows that including the possibility to weigh gene similarity changes the values of all other genes significantly in lattices (resp. RRN networks). For m=1 , cooperation is strongly determined by the ( K ) gene, and genes for direct reciprocity and constant response becomes negative or neutral. The latter implies that most agents will not cooperate in one-shot interactions with unrelated individuals, as shown in Fig. 7.10, demonstrating a significant difference from the agents without the K gene. There still is a mostly positive response for indirect reciprocity and a negative for punishment, while the weight given to participants payoff inverts. This result points to a compelling message: when heuristics can evaluate genetic relatedness, the ones that do that will have a higher reproduction, therefore resulting in more adapted heuristics. Nonetheless, information from past interactions is still required, with punishment and reciprocity playing a role. 7.2 conclusions Natural selection has shaped the evolution of all sort of life forms. Advantageous strategies endure while others dwindle in a never-ending process of adaptation. Fundamental questions regarding the emergence of cooperative behaviour in social dilemmas have to be studied 134 modelling the evolution of cooperation Figure 7.8:Evolution of heuristics with kin identification on LTT. A Fraction of cooperative actions at the steady state as a function of the mutation probability. Colours and shapes correspond for different memory ( m ) values. Averages plus .95 confidence interval of 100 realizations are presented for each mutation ( pmut ) value. B Densities of genes values for simulations on LTT graphs for pmut =0.05 and m=1 . The vertical dashed lines separate the regions wherein the probability to cooperate would be smaller (gene value smaller than 0) and greater (gene value smaller than 0) than 0.5. 7.2 conclusions 135 Figure 7.9:Evolution of heuristics with kin identification on RRN. A Fraction of cooperative actions at the steady state as a function of the mutation probability. Colours and shapes correspond for different memory ( m ) values. Averages plus .95 confidence interval of 100 realizations are presented for each mutation ( pmut ) value. B Densities of genes values for simulations on RRN graphs for pmut =0.05 and m=1 . The vertical dashed lines separate the regions wherein the probability to cooperate would be smaller (gene value smaller than 0) and greater (gene value smaller than 0) than 0.5. 136 modelling the evolution of cooperation LTT RRN 0.05 1 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 0e+00 2e+05 4e+05 6e+05 0e+00 2e+05 4e+05 6e+05 ρoneshot count Figure 7.10:Cooperation probability in one-shot games for the model with the kin identification gene . Distributions are calculated over agents of the final generation for m=1 in a lattice (left panel) and in random regular networks (right panel). Probability is calculated considering that agents do not have access to other participants information, thus, only β0 is used in the sigmoid. Top panels show distributions for pmut =0.05 and bottom panels for pmut =1. in the light of evolutionary mechanisms. Undoubtedly, emerging behaviour is intrinsically dependant on the individuals under study, e.g., humans commonly cooperate in large societies composed of unrelated individuals, while groups of animals are hardly greater than a few hundred [3]. In particular, variance in humans is especially relevant, as behaviour is deeply affected by the specifics of the interactions and the culture of the individuals [15,40]. Moreover, given that it is an emergent phenomenon, behaviour can be deeply affected by the complex topology of interactions [117]. In an attempt to provide a framework for such scenarios, here we explore a model that allows unravelling what could be the drivers of cooperation by a heuristics selection process. By exploring heuristics that make use of agents behavioural information to stochastically determine their decisions in iterated prisoners’ dilemma games across generations, we have shown that, in a feasible environment, evolution will drive heuristics towards cooperation even when defection is expected for pure strategies. In these scenarios, reciprocity and punishment are the main ingredients of cooperators’ decision-making, and most strategies will follow conditional cooperation. The fraction of cooperative decisions decreases with an increase in the mutation rate, nonetheless, for small mutation rates the system reaches a cooperative equilibrium. Without mutation, the configuration of the initial state is critical and the system can get trapped in equilibria of meagre cooperation. Increasing the memory of individu-