Climate clubs: An experimental study of Nordhaus' proposal to mitigate climate change

Climate clubs: An experimental study of Nordhaus’ proposal to mitigate climate change Supplementary Information Alberto Antonioni1,∗, Antonio Cabrales2,´ Angel S´anchez1,3 1Grupo Interdisciplinar de Sistemas Complejos, Carlos III University of Madrid, Spain 2Economics Department, Carlos III University of Madrid, Spain 3Instituto de Biocomputaci´on y F´ısica de Sistemas Complejos (BIFI), Universidad de Zaragoza, Zaragoza, Spain ∗Corresponding author: [email protected] This document provides supplementary material describing the full experimental interface presented to participants in the study. Each screen is represented in sequence, as shown to subjects during the experiment. In the following sections, additional results are reported. 1 Experimental instructions (translated from Spanish) CONSENT TO PARTICIPATE IN RESEARCH You are about to participate in a research study conducted by Anxo S´anchez, Professor of Applied Mathematics at the Department of Mathematics, Universidad Carlos III de Madrid. Your participation in this study is entirely voluntary. Please read the following information carefully and ask about anything you do not understand before deciding whether to participate. PURPOSE OF THE STUDY Our experiments are generally part of the IBSEN project, funded by the EU and designed to help understand human behavior. More information about the objectives of IBSEN and the expected advances in knowledge can be found at http://www.ibsen-h2020.eu. The specific purpose of this experiment is to collect information about collective behavior in groups of people. PARTICIPANTS General population aged 18 or older. PROCEDURES If you volunteer to participate in this study, you will be asked to make simple decisions through this computer or mobile interface, in a context where such decisions will affect your chances of obtaining a financial reward as well as the rewards of other participants. Your decisions will remain anonymous and cannot be associated with your identity, and you will not incur any financial loss. You will receive a fixed amount of 2 euros for your participation, plus an additional variable amount depending on your decisions and those of the other participants. On average, participants earn around 15 euros, but the actual amount may vary and there is no guaranteed minimum other than the fixed participation fee. Payment will be made through PayPal, so you will need to have an active PayPal account. POSSIBLE RISKS AND DISCOMFORTS There are no foreseeable risks or discomforts. CONFIDENTIALITY Data about your actions during the experiment will be collected and used for research purposes. These data will be stored without being linked to your personal identity and will be placed in an Open Data Repository after the study is completed, to share with other researchers and not for commercial purposes, in compliance with EU research policy obligations. VOLUNTARY PARTICIPATION AND WITHDRAWAL Your participation in this research study is voluntary. You may refuse to participate without penalty. If you decide to participate, you are free to stop at any time without penalty, simply by quitting the interface and/or informing the researcher. If you do not complete the experiment, you will not receive any payment. By participating in the experiment, you declare that you are at least 18 years old and fully capable and competent to understand the terms and conditions of this experiment. RESEARCHER IDENTIFICATION If you have any questions or concerns about this research, please contact us at [email protected]. BASIC DATA PROTECTION INFORMATION DATA CONTROLLER: Universidad Carlos III de Madrid. PROCESS IDENTIFICATION: Social Behavior (GISC) PURPOSE: To conduct experiments on human behavior with economic incentives. The experiments present hypothetical situations to voluntary participants who receive payment based on their actions. The data are necessary to make payments and justify expenses to the funding entity. EXERCISE OF RIGHTS: You may exercise your rights of access, rectification, erasure, restriction, portability, and objection by sending an email to dp[email protected]. ADDITIONAL INFORMATION: You may consult additional and detailed information on our Privacy Policy at https://www.uc3m.es/ protecciondedatos. I have read the information provided above. By clicking the button below, I voluntarily agree to participate in this research study under the conditions described. Screen 1 1 WELCOME Please wait while the other participants connect. You will be able to read the experiment instructions for 15 minutes starting from the official beginning time of the session. Important: We suggest that you refresh the page from time to time to ensure your browser functions correctly throughout the experiment. Please remain on this screen until the experiment begins. Screen 2 WELCOME TO THE EXPERIMENT On the next page you will read the experiment instructions. A shortened version of these instructions will remain available throughout the experiment. You have 15 minutes to read the two instruction pages. The experiment will start exactly at 16:15 (Madrid time). Important: Once you move to the second instruction page, you will not be able to return to the first. Please click “Next” when you are ready. NEXT Please proceed when prepared. Screen 3 2 GENERAL INSTRUCTIONS Important: All the points you earn will be converted into real money at the rate of 50 points = 1 EUR, plus an additional payment of 2 EUR for completing the entire experiment. The experiment consists of 15 rounds, during which you will belong to a group of 6 participants, that is, you and five other people. Within each group, two of the six participants will have Profile A, while the other four will have Profile B. The profile of a participant determines the initial amount received at the beginning of each round. Each participant’s profile remains the same throughout the entire experiment. At the beginning of each round, participants with Profile A receive 20 points, while those with Profile B receive 10 points. You will be informed of your profile before the first round begins. Each round consists of three phases: 1. Commitment phase 2. Implementation phase 3. Contribution phase You must make your decision within 30 seconds in each phase. If you fail to decide within this time limit, the system will make a random decision for you. Before explaining each phase in detail, let us first see how you can earn points during the experiment. In each round, a coalition may be formed among the participants in your group who decide to do so. All participants who join the coalition will contribute all their initial points to a common fund, while those who do not join the coalition may freely decide how many points to contribute. At the end of the round, the total number of points in the common fund is multiplied by 3and distributed among all members of the group according to the following rule: Participants with Profile A receive one quarter of the fund, while those with Profile B receive one eighth. For example, if the common fund contains 40 points, it is multiplied by 3 to make 120 points. Participants with Profile A then receive 30 points each, and those with Profile B receive 15 points each. In addition, at the end of each round, if a coalition has been formed, you will gain or lose additional points calculated as follows: Let Xbe the weighted number of participants in the coalition, where Profile A participants count as 2and Profile B participants as 1. Let Y= 8 −Xbe the weighted number of those not in the coalition. At the end of the round: •Participants in the coalition gain Y/2 additional points. •Participants not in the coalition lose Xpoints. For example, if a coalition is formed by two participants—one with Profile A and one with Profile B—then X= 2 + 1 = 3 (and Y= 5). Thus, coalition members gain Y/2=2.5 points, while those outside the coalition lose X= 3 points. [ONLY VISIBLE FOR TREATMENT 4] Please click “Next” when you are ready to continue. NEXT Take your time to read carefully and proceed when prepared. Screen 4 3 GENERAL INSTRUCTIONS (PHASES) [PLEDGING AND COMMITMENT PHASES WERE NOT PRESENT FOR TREATMENT 1] 1) Pledging Phase In this phase of each round, you decide whether you want to commit to joining the coalition. This decision will be recorded in your commitment history throughout the experiment. You will see the history of commitment decisions of all participants in your group, displayed as follows: Each row represents one participant, and you are highlighted in bold (participant B1 with profile B in this example). “S” means that the participant committed to joining the coalition in that round, “–” means that they did not commit. In this phase, your decision to commit to the coalition is not final and can be reconsidered in the next phase. 2) Commitment Phase In this phase, only participants who decided to commit (“S”) in the previous phase take part; those marked with “–” do not participate. Here, you decide whether to confirm your commitment to join the coalition. The coalition is formed only if all participants who had committed confirm their decision [ONLY VISIBLE FOR TREATMENT 3 AND 4].Your confirmation or withdrawal will be added to your commitment history. You will be able to see the history of commitments for your group during the last five rounds, displayed as follows: In this table, “C” means the participant confirmed their commitment, “R” means they withdrew, and “–” means they could not participate in this phase because they had not committed in the previous one. In this example, the coalition of four people is formed only in the fifth round, as shown by the bold “C” symbols. 3) Contribution Phase If the coalition is formed in the previous phase, the coalition members do not make decisions in this phase, since they have agreed to contribute their entire initial endowment. If the coalition is not formed, then all participants take part in this phase. In this phase, you decide how many points to contribute to the common fund, between 0 and your entire endowment. As with previous decisions, your contribution will be stored in your contribution history for the last five rounds. You will be able to see the contribution history of your group during the experiment as follows: Contributions in bold represent participants who contributed their full endowment because they joined the coalition. Values in normal font represent freely chosen contributions. At the end of this phase, you will see your payoff for the current round, which consists of: •The points you did not contribute to the common fund. •Your share of the common fund according to your profile weight. •Plus or minus the additional points earned through coalition formation (as explained previously). For example, in the table above, the total common fund in round five reached 68 points, which multiplied by 3 results in 204 points. Participant B1, who joined the coalition and thus contributed their entire endowment, receives one-eighth of 204 points, that is, 204/8 = 25.5 points,plus Y/2=3/2 = 1.5 points additional, for a total of 27 points. Participant A2, who did not join the coalition and contributed freely, receives one-quarter of 204 points (204/4 = 51 points), plus the 4 points they kept, minus X=5 points, for a total of 52 points [ONLY VISIBLE FOR TREATMENT 4]. A shortened version of these instructions will remain available throughout the experiment for your reference. Please click “Next” when you are ready to make your first decision. Remember, you must decide within 30 seconds in each phase; otherwise, the system will make a random decision for you. NEXT You may now proceed to the decision phase. Screen 5 4 PLEASE WAIT UNTIL ALL PARTICIPANTS FINISH READING THE INSTRUCTIONS [PLEDGING AND COMMITMENT PHASES WERE NOT PRESENT FOR TREATMENT 1] Summary of the Experiment •50 points = 1 EUR. •You will participate for 15 rounds in the same group of 6 people. •In each round, participants of type Ahave a weight of 2and receive 20 points, while participants of type Bhave a weight of 1and receive 10 points. •The common fund is multiplied by 3and distributed among all participants according to the following scheme: •The coalition is formed only if all participants confirm their commitment. [ONLY VISIBLE FOR TREATMENT 3 AND 4] •Participants in the coalition contribute their entire endowment. •X= total weight of the participants forming the coalition. •Y= total weight of the participants not in the coalition. •If the coalition is formed: –If you are part of the coalition, you gain Y / 2 additional points. –If you are not part of the coalition, you lose X points. [ONLY VISIBLE FOR TREATMENT 4] •Commitment phase: you can choose to commit to forming the coalition. •Implementation phase: you can confirm your commitment. •Contribution phase: you can decide how much to contribute to the common fund. Please wait until all participants have completed reading these instructions. The experiment will continue automatically once everyone is ready. You may remain on this screen until the next phase begins. Screen 6 THE EXPERIMENT BEGINS NOW! On the next screen, you will make your first decision in the experiment. Remember that you must make your decision within 30 seconds in each phase. If you do not decide within this time, the system will make a random decision for you. Please click “Next” when you are ready. NEXT You may now proceed to your first decision. Screen 7 5 ROUND 6 — PLEDGING PHASE [example case for treatment 4] In the previous round, the coalition was formed, and you were part of it. Your contribution was 10 points. The common fund collected a total of 72 points, which multiplied by 3yields 216 points. As a type B participant, you earned: 0 points not contributed, plus 216/8 = 27 points from the common fund, plus Y/2 = 2 additional points, for a total of 29 points. You are the Participant B1. Your profile is Type B, and you receive an endowment of 10 points per round. Your total accumulated earnings so far: 114.50 points. Commitment Table Participant 5 4 3 2 1 A1 C C C – R A2 – – C C– B1 (You) C C S CS B2 – – C – C B3 CS – C– B4 – S R – C Contribution Table Participant 5 4 3 2 1 A1 20 20 10 8 20 A2 18 20 20 20 14 B1 (You) 10 10 6 10 8 B2 6 10 8 0 0 B3 10 10 6 10 0 B4 8 6 10 0 2 Legend: S : committed; – : not committed; C : confirmed commitment (Cif the coalition was formed); R : withdrew commitment. Now please indicate whether you want to commit to joining the coalition in this round. YES — COMMIT NO — DO NOT COMMIT NEXT Reminder of the Rules: •50 points = 1 EUR. •6 participants: 2 of type A (weight 2, endowment 20) and 4 of type B (weight 1, endowment 10). •The common fund is multiplied by 3 and shared among all proportionally to their weight. •The coalition forms only if all committed players confirm. •X= total weight of the participants forming the coalition. •Y= total weight of the participants not in the coalition. •Coalition members contribute all their points and receive extra Y/2. •Non-members lose Xpoints. Screen 8 6 ROUND 6 — IMPLEMENTATION PHASE [example case for treatment 4] Only participants who pledged in the previous phase take part now. Please confirm your commitment to join the coalition. The coalition is formed only if all committed participants confirm their decision. You have 30 seconds to decide; otherwise, the system will choose at random. [in the case the participant did not commit in the previous phase, this phase is not shown.] You are Participant B1 (Type B) with a per-round endowment of 10 points. Commitment Table Participant 6 5 4 3 2 A1 SCC C – A2 – – – C C B1 (You) SCC – C B2 – – – C – B3 S C– – C B4 – – S R – Contribution Table Participant 6 5 4 3 2 A1 – 20 20 10 8 A2 – 18 20 20 20 B1 (You) –10 10 6 10 B2 – 6 10 8 0 B3 – 10 10 6 10 B4 – 8 6 10 0 Legend: S : committed; – : not committed; C : confirmed commitment (Cif the coalition was formed); R : withdrew commitment. Please choose whether to confirm your commitment for this round: CONFIRM WITHDRAW Please click “Next” when you are ready. NEXT Reminder of the Rules: •50 points = 1 EUR. •6 participants: 2 of type A (weight 2, endowment 20) and 4 of type B (weight 1, endowment 10). •The common fund is multiplied by 3 and shared among all proportionally to their weight. •The coalition forms only if all committed players confirm. •X= total weight of the participants forming the coalition. •Y= total weight of the participants not in the coalition. •Coalition members contribute all their points and receive extra Y/2. •Non-members lose Xpoints. Screen 9 7 ROUND 6 — CONTRIBUTION PHASE [example case for treatment 4] The coalition has been formed and you are part of it. Therefore, in this round you automatically contribute your entire endowment of 10 points. [otherwise, the participant freely decides their contribution between 0 and their total endowment.] Commitment Table Participant 6 5 4 3 2 A1 C C C C – A2 – – – C C B1 (You) C C C – C B2 – – – C – B3 C C – – C B4 – – S R – Contribution Table Participant 6 5 4 3 2 A1 – 20 20 10 8 A2 – 18 20 20 20 B1 (You) –10 10 6 10 B2 – 6 10 8 0 B3 – 10 10 6 10 B4 – 8 6 10 0 Legend: S : committed; – : not committed; C : confirmed commitment (Cif the coalition was formed); R : withdrew commitment. Please click “Next” to continue. NEXT Reminder of the Rules: •50 points = 1 EUR. •6 participants: 2 of type A (weight 2, endowment 20) and 4 of type B (weight 1, endowment 10). •The common fund is multiplied by 3 and shared among all proportionally to their weight. •The coalition forms only if all committed players confirm. •X= total weight of the participants forming the coalition. •Y= total weight of the participants not in the coalition. •Coalition members contribute all their points and receive extra Y/2. •Non-members lose Xpoints. Screen 10 After Screen 10, participants start a new round from the pledging phase (Screen 8) until reaching Round 15 and then advancing to the final part (Screen 11). 8 Metric T4 vs T1 T4 vs T2 T4 vs T3 Median SD (T4) 0.131 0.131 0.131 Median SD (ref) 0.118 0.177 0.198 Diff of means 0.001 −0.051∗−0.074∗ t-stat 0.07 -2.81 -2.85 df 7.53 8.86 8.52 p-value 0.942 0.021 0.020 95% CI low -0.037 -0.091 -0.134 95% CI high 0.039 -0.010 -0.015 Table S6: Welch t-tests on group-level SD over rounds: T4 vs T1, T2, T3. Entries compare the dispersion of group mean contributions across rounds (lower SD = more stability). Diff of means is the difference in mean SD over rounds (T4 minus reference): negative values indicate T4 is more stable. The Welch tstatistic, degrees of freedom (df), two-sided p-value, and 95% CI refer to the mean difference. 15