An Economic Analysis of Collaboration Between Gompeting Firms

Stickel, Eberhard Article An Economic Analysis of Collaboration Between Gompeting Firms Kredit und Kapital Provided in Cooperation with: Duncker & Humblot, Berlin Suggested Citation: Stickel, Eberhard (2004) : An Economic Analysis of Collaboration Between Gompeting Firms, Kredit und Kapital, ISSN 1865-5734, Duncker & Humblot, Berlin, Vol. 37, Iss. 2, pp. 202-222, https://doi.org/10.3790/ccm.37.2.202 This Version is available at: https://hdl.handle.net/10419/293502 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Introduction Decision makers need to understand the economics of collaboration in order to be able to evaluate the potential of collaborative technology Collaboration between different actors may occur within a firm's boundary or across it. Throughout the paper the focus lies on collaboration across the boundaries of firms. The economic effects of collaboration between firms located along different phases of the value chain (typically supplier-purchaser-relationships) have been studied in the literature extensively. Usually, transaction cost theory is applied to derive the "optimal" institutional structure (cf. Williamson (1975)). Basic institutional arrangements are hierarchy, market and network cooperations (cf. demons et al. (1993)). The use of collaborative technology may be especially useful in case of network cooperations. As Clemons et al. point out, the use of IT triggers a move towards such cooperations (move-to-the-middle-hypothesis). A more formal economic analysis of interorganizational systems is presented in Clemons/Kleindorfer (1992). Collaboration between competing firms is a problem that has not yet been studied in such detail. As it is well-known, strategies of firms may be seen as a mixture of cost reduction, product differentiation and improvement of decision making and/or planning. Information technology may help a firm to create sustaining competitive advantages over competitors (examples are contained in Clemons (1991)). Sustainability is an important issue to defend investments from being imitated too quickly (see Kettinger et al. (1994)). Based on this observation it is not clear whether collaboration between competing firms is useful. Generally, collaboration between competing firms may occur in many ways. Some examples are joint use of complex technological or marketing processes, bundling products or setting standards. Collaboration Kredit und Kapital 2/2004 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.37.2.202 | Generated on 2023-01-16 13:21:00 An Economic Analysis of Collaboration Between Competing Firms 203 typically requires sharing information and know how, as well as resources. In literature collaboration problems are usually studied with the help of methods from microeconomics and game theory. It turns out that the most important factors affecting the usefulness of collaboration are as follows: • Market structure. If perfect competition prevails collaboration is of limited use. No single firm or proper subsets of firms may influence market prices and/or quantities. In a monopolistic environment there obviously is no room for collaboration. Consequently, the interesting market structure is an oligopoly. Depending on the kind of products offered and the way an equilibrium is obtained, price or quantity setting oligopolies may be distinguished (Bertrand or Cournot oligopolies, cf. Pindyck/Rubinfeld (1992, pp. 430) and Martin (1988)). • Product relationship. Products offered may be substitutes or complements. In general, we would expect that products of competing firms are substitutes. Product differentiation, however, allows to vary the degree of possible substitution. • Distribution of knowledge and ability. The distribution of knowledge and ability is closely related to the possibility of generating sustaining competitive advantages (cf. Choudhury/Sampler (1997)). If a firm has specific knowledge or specific abilities that competitors do not have it may use these skills to outperform competing firms. • Kind and degree of uncertainty faced by competing firms. Basically we may distinguish uncertainty with respect to common or private variables. As an example consider demand parameters. They are called common or public variables since they directly affect profits but are not firm specific. On the other hand variable costs are an example of private variables (cf. Jin (1994, p. 323)). They are firm specific. Of course, knowledge of rival's variable costs may affect a firms own decisions since it may predict rival's behavior more precisely. • Risk preferences of competing firms. It is assumed that decision makers are risk averse. Hence they would not maximize expected profits as if they were risk neutral but expected utility of profits. The results obtained depend on the assumptions made about the factors identified above. They partially differ or even contradict each other. Important factor combinations have not yet been studied in detail. An example is the case of an oligopoly with differentiated products, demand Kredit und Kapital 2/2004 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.37.2.202 | Generated on 2023-01-16 13:21:00 204 Eberhard Stickel uncertainty and risk averse managers. Note, that this seems to be the case that is mostly found in real life. In this paper the case of differentiated products, demand uncertainty and risk averse managers will be studied in detail. For the sake of simplicity the analysis will be restricted to the case of two competing firms (duopoly). It is possible but tedious to extend the analysis to the case of more than two competitors. The analysis is carried out with the help of a microeconomic model that will be presented in the third section. The basic assumption is that collaboration occurs through knowledge and information sharing, common information collection and/or interpretation. In order to share information, knowledge and know-how collaborative technology is usually applied. Joint application development and joint use of resulting information systems, as well as interorganizational information systems in general are typically covered by such an analysis. Joint application development bundles development capabilities in an effort to reduce development costs. Typically specific know how and information is shared between the cooperating development partners. Hence, in case of competing developers, it is necessary to compare the benefits associated with reduced costs to possible disadvantages faced by disclosing information and know how. In this paper we will assume that information is shared via joint application development and/or joint use of such systems. Note, that in our context collaboration may be characterized as being pre-competitive. It should not be mixed up with collusion which may be legally restricted or even forbidden. A formal model will be developed in the sequel. Techniques from game theory allow to solve the corresponding optimization problems. The model will be analyzed in a simple setting in order to be able to derive closed-form solutions which may be handled more conveniently. Generalizations which make the model more realistic are of course possible and will be indicated. Usually, more general settings will not allow the derivation of closed-form solutions. Then numerical or simulation techniques have to be used. However, the results presented for the simple case will change only slightly in the more general cases. To make the paper accessible to the "non-technical" reader the formal derivations have been placed in the appendix of the paper. Kredit und Kapital 2/2004 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.37.2.202 | Generated on 2023-01-16 13:21:00 An Economic Analysis of Collaboration Between Competing Firms 205 In the second section results obtained so far in literature will be reviewed. Section IV. discusses the results obtained with the help of the model developed in section III. Finally, section V. presents a conclusion. Throughout the paper we will assume risk averse decision makers. Such decision makers prefer a secure payment of t/$ to a lottery that pays 0$ with probability V2 and 2y$ with probability V2. On the first view, this seems to contradict common assumptions, e.g., in portfolio management. Here, investors, although risk averse, would choose their risky portfolios as if they were risk neutral. The reason for this is that risk (in portfolio theory the so-called unsystematic risk) may be diversified away. Investors only need to bare the systematic risk which can never be diversified away. Hence, it seems natural to assume that a rational company maximizes its expected profits. In larger companies, however, decisions are usually delegated by absentee owners to managers. The compensation of such managers is very often tied to profits. This fact, as well as possible opportunistic behavior and asymmetric information, suggest that managers behave more or less risk averse (cf. Kao/Hughes (1993, p. 103)). Consequently, expected utility of profits is maximized instead of expected profits. A first result of our analysis shows that maximization of expected utility may lead to different optimal actions than maximization of expected profits. While the latter in general is a simple optimization problem, maximization of expected utility requires knowledge of the utility function of the decision maker. Note, that this is a more difficult and complex problem. If costs of information sharing are sufficiently low, information sharing in general is beneficial if development know how is equally distributed. This is an expected result since then development costs may be reduced. This result, however, changes significantly if know how for development is not equally distributed between the competitors. In this case situations occur that are well-known from the treatment of "prisoner-dilemma-situations" (for a treatment of this game-theoretic problem cf. Rasmussen (1995)). Results then strongly depend on the degree of risk aversion and the market structure and nearly all "prisoner-dilemma-situations" may be constructed by suitably choosing the model parameters. First mover and follower strategies are then optimal choices depending on risk aversion of the decision makers and market structure. Kredit und Kapital 2/2004 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.37.2.202 | Generated on 2023-01-16 13:21:00 206 Eberhard Stickel In some instances, the results obtained will be surprising and contradict common expectations. It can be shown, e.g., that the use of information to reduce uncertainty may be harmful for a company. Firms are paid for taking risks. If they try to reduce such risks profits and expected utility may decrease (even if risk is reduced at zero costs, see e.g. Palfrey (1982)). Once again, such surprising results show the importance of understanding the economic effects of collaboration before deciding on investments in collaboration technologies. II. Previous Work In literature the effects of collaboration between competitors are not directly analyzed (except collusion). There is some literature on the effects of information sharing with respect to private or common variables. The question whether it pays off to share such information is important to analyze possible effects of collaboration with respect to information collection and/or sharing by means of suitable information systems. Existing literature may be roughly classified into the categories homogeneous versus heterogeneous market environment, consideration of risk aversion or assumption of risk neutrality and analysis of uncertainty of private or common model parameters. Altogether, eight categories result by combining these classes. In case of homogeneous products (no product differentiation) firms usually behave as price takers and set quantities accordingly. The most simple price-demand-function is linear and given by p = a-b{q1 +q2). Here a and b are parameters to be specified, p is the price that results if the z-th firms offers quantity on the market. Uncertainty with respect to common (public) variables may be introduced by allowing a to be a random variable. Uncertainty with respect to private variables is introduced by treating the variable costs Ci of each firm as random variables. If risk aversion of decision makers is not considered each firm maximizes expected profits. For the z-th firm profits in the most simple setting are given by Kredit und Kapital 2/2004 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.37.2.202 | Generated on 2023-01-16 13:21:00 An Economic Analysis of Collaboration Between Competing Firms 207 11; = {a - b(qi + q2) - Ci)qi. Note, that in this simple setting fixed costs are not considered. Moreover, economies of scale (decreasing variable costs) are not possible. In case of risk aversion decision makers do not maximize expected profits but the utility of expected profits. For the sake of computational simplicity constant absolute risk aversion is usually assumed. The utility function of the ¿-th decision maker is then given by Ui(x) = 1 - exp(-7ix). The degree of risk aversion of the decision maker is measured by % > 0. Higher values of this parameter result in a higher degree of risk aversion. Fried (1984) investigates incentives for information production and disclosure in a duopolistic environment. The focus is on unknown variable costs. Variable costs have two components of uncertainty. First, there is a common component related to the economy, second, there is a firm-specific component. Fried assumes, that decisions are first made about information production and disclosure. The decision made by each firm is known and enforceable. Then four scenarios need to be analyzed: (1) Neither firm F\ nor firm F2 produces and discloses private information, (2) firm Fi discloses while firm F2 does not, (3) the roles of firm Fi and F2 in the second scenario are interchanged and (4) both firms produce and disclose information. Each scenario is analyzed in detail and a so-called Nash-equilibrium is determined. In such an equilibrium neither firm has an incentive to change its strategy. For details of Nashequilibria refer to Rasmussen (1995, pp. 15-29 and pp. 276-279). When firm Fi discloses information which firm F2 does not have the result depends on how variable costs are composed of private and common factors. Disclosure of private cost components is usually beneficial, disclosure of common components generally does not pay off. Gal-Or (1985) and Li (1985) study the effects of information sharing associated with an uncertain demand parameter a When a firm observes a signal of low demand (this corresponds to a low value of the parameter a) disclosure of this information may prevent its competitor from overproducing. On the other hand, disclosure of a signal indicating high demand may result in a higher production of the competitor. Both authors investigated which effect was dominating. Their result suggests that information sharing is not an optimal strategy. Gal-Or assumed a Kredit und Kapital 2/2004 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.37.2.202 | Generated on 2023-01-16 13:21:00 208 Eberhard Stickel normal distribution of the parameter a, Li allowed more general probability distributions. Li also analyzed the case of sharing private cost information and confirms the results of Fried. To summarize, sharing information about private parameters pays off, sharing information about common parameters does not. Unfortunately, these results change if risk aversion is considered. As it was already indicated, the delegation of decisions from owners to managers naturally introduces risk aversion. Palfrey (1982) provided first insights into this situation. He showed that even the private use of information may be harmful. In particular, a firm that is less risk averse than its competitor(s) is rewarded for taking higher risks. If such a firm tries to reduce risk by using information the more risk averse competitor does not have, it is usually worse off afterwards. More work on the subject stems from Hviid (1989) and Kao/Hughes (1993). Hviid investigates the incentives of a risk averse firm to share information. He showed that the results obtained in the case of risk neutrality need not to be true anymore. Hviid analyzed demand uncertainty and treated the parameter a as a random variable. Kao and Hughes extended the analysis of Hviid to the case of sharing firm-specific cost information. To summarize, it can be shown that if risk aversion is considered there also may be incentives for collaboration. In most companies managers will behave as risk averters. This is the situation that usually prevails in practice. We now turn to the case of heterogeneous products. In that case firms usually set prices. Now, each firm has its own price-demand function. In the most simple case we obtain for the z-th firm the expression (1) qi = a-b(pi + 6(pi-p)). As in the homogeneous case a and b are parameters to be specified. 6 models the degree of substitutability of the products offered in the market place. Small values of 6 > 0 correspond to a low degree of possible substitution (heterogeneous or highly differentiated products), high values to a high degree of substitution respectively (homogeneous products). p is the arithmetic mean of the prices of all competing firms. Kredit und Kapital 2/2004 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.37.2.202 | Generated on 2023-01-16 13:21:00 An Economic Analysis of Collaboration Between Competing Firms 209 Thus, it is obvious how the model extends to the case of an arbitrary oligopoly. Gal-Or (1986) has analyzed information transmission in heterogeneous market environments for risk neutral decision makers. Uncertainty was introduced with respect to the variable costs of each firm. Uncertain costs are composed of two components, a firm-specific private and a common one. Note, that competition is based on prices now. This is why firms have an incentive to share information about common parameters. It does not pay off to share information about private parameters. This is in contrast to the homogeneous product case. Gal-Or also analyzed the case of a heterogeneous oligopoly where quantities are set and prices are determined via the price-demand-function. The systems of price-demand-functions given in (1) is then inverted. Due to the stochastic nature of some parameters the two models are not equivalent (cf. Klemperer/Meyer (1986)). In that case firms will reveal firm-specific but not common information. This result is in line with the homogeneous case. III. Model Building In the following the probably most relevant case of a market with heterogeneous products where prices are set and decision makers are risk averse will be considered. The importance of heterogeneous markets and the assumption of risk aversion was already motivated. Klemperer/Meyer (1986) have shown that generally price competition is preferred by firms in an oligopolostic market if the slope of the marginal cost curve is rather flat. Since we assume constant variable costs the slope of marginal costs is zero everywhere and the result of Klemperer and Meyer applies. Also note, that price competition prevails in a lot of interesting markets. Examples are the airline and automotive industry, as well as the financial services sector. The starting point of our analysis is formula (1). By neglecting a constant factor (numéraire) in (1) we may assume without loss of generality that 6 = 1. Then, the demand-function of firm Fi may be rewritten as (2) qi = a + apj-Ppii with 0 < a = ¡3 - 1 and i^j. In the same way as the parameter 6 in (1) a determines the degree of heterogeneity of the market under consideration. Uncertainty will be introduced to our model by treating a as a Kredit und Kapital 2/2004 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.37.2.202 | Generated on 2023-01-16 13:21:00 216 Eberhard Stickel The presented model may be extended in a variety of ways in order to make it more realistic. Other distributions of a may be used. In particular it makes sense to restrict a to a certain interval [A,B]. Then the use of a beta-distribution would allow to model nearly arbitrary distributions of a with a single peak. The results remain the same but closed-form solutions may not be derived anymore. Of course it is possible to use other price-demand and/or utility functions too. Numerical simulations have been carried out with quadratic demand and utility functions. Again, the spirit of the results does not change. Another line of generalization is to use firm-specific parameters Again, this does not significantly change the results. Finally we may investigate the effects of different cost structures, as well as the effects of announcing prices earlier than the competitor. In general, a firm with lower variable costs or a firm that announces its decisions earlier, faces an advantage. Depending on which firm has lower costs or announces earlier the results presented may be offset by these effects. For decision makers it is important to understand the economical effects of collaboration. Factors that need to be analyzed have been identified in the paper. Moreover, decision makers should use models from game theory in order to anticipate rival's behavior. Of course the simple model that was presented in this paper is only a first step towards more sophisticated simulation approaches with more realistic assumptions and data used. References Choudhoury, V., Sampler, J.: Information Specifity and Environmental Scanning: An Economic Perspective. MIS Quarterly 21, No. 1, 1997, pp. 25-53. - demons, E.: Evaluation of Strategic Investments in Information Technology. Comm. of the ACM 34, No. 1, 1991, pp. 22-36. - Clemons, E., Kleindorfer, P.: An Economic Analysis of Interorganizational Information Technology. Decision Support Systems 8, 1992, pp. 431-446. - demons, E., Reddi, S. Row, M.: The Impact of Information Technology on the Organization of Economic Activity - The "Move to the Middle" Hypothesis. Journal of Management Information Systems 10, No. 2, 1993, pp. 935. - Copeland, T., Weston, J.: Financial Theory and Corporate Policy. 2nd Ed., Reading, MA. (1983). - Fried, D.: Incentives for Information Production and Disclosure in a Duopolistic Environment. Quarterly Journal of Economics 99, 1984, pp. 367-381. - Gal-Or, E.: Information Sharing in Oligopoly. Econometrica 53, No.2 , 1985, pp. 329-343. - Gal-Or, E.: Information Transmission - Cournot and Bertrand Equilibria. Review of Economic Studies 53, 1986, pp. 85-92. - Hviid, M.: Risk-Averse Duopolists and Voluntary Information Transmission. Journal of Industrial Economics 38, No. 1, 1989, pp. 49-64. - Jin, J.: Information Sharing Through Sales Report. Journal of Industrial Economics 42, No. 3, 1994, pp. 323Kredit und Kapital 2/2004 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.37.2.202 | Generated on 2023-01-16 13:21:00 An Economic Analysis of Collaboration Between Competing Firms 217 333. - Kao, J., Hughes, J.: Note on Risk Aversion and Sharing of Firm-Specific Information in Duopolies. Journal of Industrial Economics 41, No. 1, 1993, pp. 103-112. - Kettinger, W., Grover, V., Guha, S.: Strategic Information Systems Revisited: A Study in Sustainability and Performance. MIS Quarterly 18, No. 1, 1994, pp. 31-58. - Klemperer, R, Meyer, M.: Price Competition vs. Quantity Competition: The Role of Uncertainty. Rand Journal of Economics 17, No. 4, 1986, pp. 405-415. - Li, L.: Cournot Oligopoly with Information Sharing. Rand Journal of Economics 16, No. 4, 1985, pp. 521-536. - Martin, S.: Industrial Economics. New York (1988). - Palfrey, T. R.: Risk Advantages and Information Acquisition. Bell Journal of Economics 13, No. 1, 1982, pp. 219-224. - Pindyck, R., Rubinfeld, D.: Microeconomics. Ed., New York (1992). - Rasmussen, E.: Games and Information. An Introduction to Game Theory. 2nd Ed., Oxford UK (1995). - Williamson, O.: Markets and Hierarchies - Analysis and Antitrust Implications. New York (1975). Appendix Lemma 1 If both firms have the same variable costs c we may assume without loss of generality that c = 0 holds. Proof. Profits of the z-th firm are given by Ui = (_pi - c)(a + apj - Ppi). Substituting pk=pk - c for k = 1,2 and using (3 = a + 1 yields 11* = pi(a + apj - (5pi + ac - (5c) = pi(a -c + afij- (3pi). This is the problem with zero variable costs if a is assumed to have a normal distribution with mean /x - c and variance a2. • Lemma 2 Let a have a normal distribution with mean \x and standard deviation a. Suppose further that a decision maker has constant risk aversion 7. The certainty equivalent C of this decision maker for the payoff c2a2 + Cia + c0 is then given by C = -ln[l + 2c2 V] + Co + m + ^ • Kredit und Kapital 2/2004 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.37.2.202 | Generated on 2023-01-16 13:21:00 218 Eberhard Stickel Proof. For the density of a normal distribution with mean ¡JL and standard deviation a we have 00 -00 Expected utility R of our decision maker is given by oo R = I exP(~y ~ exp(-7(c2a2 + Cia + c0)]da -00 oo 1 f la — /x2 = 1 - nr- / exp(- — ( ) ) exp(-7(c2a" + cxa + c0)da = 1 -1. yziva J La -oc Using standard techniques from calculus the last integral I may be evaluated to get By assumption the utility function of our decision maker is given by u(x) = 1 - exp(-7o;). Consequently ln(l - u(x)) x = — . 7 For the certainty equivalent this yields C = u\R)=u\l-l) = -]^-. 7 From this the claim readily follows. • Lemma 2 may be used to compute the certainty equivalent for firm Fi in scenarios 2 and 4 and for firm F2 in scenarios 3 and 4. Expected profits are quadratic functions of a. To see this, note, that by (4) the right factor is a linear function of a. In scenarios 2 and 4 for the first and scenarios 3 and 4 for the second firm pi(a) and p2(a) are also linear funcKredit und Kapital 2/2004 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.37.2.202 | Generated on 2023-01-16 13:21:00 An Economic Analysis of Collaboration Between Competing Firms 219 tions of a. Then, the product in (4) is a quadratic function of a and may be rewritten in the form c2a2 + C\a + c0 with suitable constants d{i = 0,1,2). Table 1 Expected Profits of Firms (ft^: Expected profits of firm F* in scenario j) ß2{ß + /yi°2)(2ß + Q +12°2)2 11 (4/?2 - a2 + 2ßa2(71 + 72) + 7i72<74)2 2 WW2 +2ft/? - ft2) + (2ß + af^o2)2 12 ±ß ß 4:ß(4:ß(2ß2 — a2) + (2ß + a)272C2)2 ß2(2ß + a)2((2/3 + q)27i^ + 2ß(2ßz - a2)) = (4/?(/?2 - a2) + (2ß + a)27i^2)2 " (2ß " <*)2 //2(^ + 72<72)(2/? + Q + 7i02)2 21 (4/?2 - a2 + 2#t2(7I + 72) + 7i72^)2 ft = P2(2/? + ft)2((2^ + a)272a2 + 2ß(2ß2 - q2)) 22 (4/?(/?2-a2) + (2/? + a)2 72a2)2 ft =£l 2 (2/3?(4^2 + 2a/? - a2) + (2/? + af-no*)2 = fct^l 23 4/? ß 4/?(4/?(2/?2 -a*) + (2ß + ft)27i<r2)2 ** (2/? - ft)2 Kredit und Kapital 2/2004 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.37.2.202 | Generated on 2023-01-16 13:21:00 220 Eberhard Stickel Table 2 Certainty Equivalents of Firms (C^: Certainty equivalent of firm F* in scenario j) Cn = ß2(2ß + jio2)(2ß + a + 72<t2)2 Ci3=-W + a)2 2(4/32 - a2 + 2^2(7i + 72) + 7i72^4)2 2(4/3(2^2 - a2) + (2ß + af^a2) Ci2=—In 271 C14 = —In 271 1 + 7i o2 2ß ß2m2ß2-a2)^(2ß + a)\o2)2 2{2ß + 71 er2)(2/?(4/?2 + 2aß - a2) + (2/9 + a)27i<72)2 1 + 2/W (2/9-a)2 ft*2 2/071 a2 + (2/? - a)' C2i = ß2{2ß + 72(72)(2/3 + q + 710"2)2 2(4/92 - a2 + 2/9a2(7l + 72) + 7i72^)2 C22 = W + a)2 2(4/9(2/92 — a2) + (2ß + a) 72er2) C23 = —In 272 C24 =^ln 272 1 + 72a2' 2/?. /¿2(4/9(2/92 — a2) + (2/9 + a)272Q'2)2 " 2(2/? + 7i<t2)(2/9(4/92 + 2a/9 - a2) + (2/9 + a)272^2)2 1 + 2/W (2/9-a^ 2ßrilo2 + (2/9 - a)2 Summary An Economic Analysis of Collaboration Between Competing Firms To understand adoption of collaborative systems, it is of great importance to know about economical effects of collaboration itself. Decision makers should be able to value potential drawbacks and advantages of collaboration. Based on this estimation, the potential of collaborative technology may be determined. Throughout the paper we are interested in the effects of collaboration across a firm's boundary. There is vast literature on economical effects of collaboration among companies situated along different phases of the value chain. At least in economical terms this seems to be a well understood problem. The situation is different with respect to collaboration between competing companies. Strategies of firms may be seen as a mixture of cost reduction, product differentiation and improvement of decision making and/or planning. In this context information technology may help a firm to create sustaining competitive advantages over competitors. It is less clear whether collaboration is of any use in such an environment. According to the economics literature, the most important factors affecting benefits of collaboration are market structure, kind and degree of uncertainty faced by the firms, their risk preferences and the type(s) of product(s) offered (homogeneous or hetKredit und Kapital 2/2004 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.37.2.202 | Generated on 2023-01-16 13:21:00 An Economic Analysis of Collaboration Between Competing Firms 221 erogeneous products). The results reported depend on the way these factors are combined. They partially contradict each other. In this paper we will analyze the most relevant case of an oligopoly with differentiated products, demand uncertainty and risk averse managers. This combination has not yet been examined in detail, although it is the most realistic case. We will present a microeconomic model and use techniques from game theory for the analysis. The way the model is constructed will allow the derivation of closed-form solutions. Results indicating whether collaboration in various areas makes sense will be obtained. This makes it possible to judge the potential of available collaborative technology. The simple model presented may be extended in a variety of ways. Some directions for possible generalization are indicated. (JEL CO, C70, L10) Zusammenfassung Eine ökonomische Analyse der Kooperation zwischen Wettbewerbern Kooperation spielt nicht zuletzt unter dem Aspekt ständig steigender Entwicklungskosten eine wichtige Rolle bei der Entwicklung von Informationssystemen. Entscheidungsträger sollten deshalb die ökonomischen Effekte derartiger Entwicklungspartnerschaften verstehen, um rationale Entscheidungen zu fällen. Im Rahmen der Arbeit werden die ökonomischen Effekte von Entwicklungspartnerschaften zwischen Wettbewerbern detailliert analysiert. Bei der gemeinsamen Entwicklungsarbeit wird natürlich oft wertvolles Wissen an Konkurrenten weitergegeben. Dies spricht gegen Kooperation, während das Einsparen von Entwicklungskosten eher dafür spricht. Insofern ist nicht klar, ob Kooperationen zwischen Wettbewerbern sinnvoll sein können. In der Literatur werden zahlreiche Modelle diskutiert. Die wichtigsten Faktoren, die eine Kooperationsentscheidung beeinflussen, sind dabei Marktund Produktstruktur, Art und Umfang der vorherrschenden Unsicherheit sowie die Risikopräferenzen der Entscheidungsträger. Die in der Literatur diskutierten Ergebnisse unterscheiden sich dabei je nachdem, wie man diese Faktoren kombiniert. Der aus Sicht der Praxis wichtigste Fall liegt bei oligopolistischer Marktstruktur, heterogenen Produkten und risikoaversen Entscheidungsträgern, die Nutzenmaximierung betreiben, vor. Dieser Fall wurde nicht zuletzt aufgrund seiner Komplexität bisher nicht umfassend analysiert und ist Gegenstand dieser Arbeit. Die Analyse erfolgt anhand eines formalen Optimierungsmodells, das die Bestimmung von geschlossenen Lösungen erlaubt. Das Modell kann in verschiedene Richtungen erweitert und so besser an die Realität angepasst werden. Résumé Une analyse économique de la coopération entre des firmes concurrentes Pour comprendre l'adoption des systèmes de coopération, il est d'une grande importance de connaître les effets économiques de la coopération elle-même. Les preneurs de décision devraient être capable d'évaluer les inconvénients et les avantages de la coopération. Sur base de cette estimation, le potentiel de la coopéKredit und Kapital 2/2004 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.37.2.202 | Generated on 2023-01-16 13:21:00 222 Eberhard Stickel ration technologique pourrait être déterminé. Dans ce travail, l'auteur s'intéresse aux effets de la coopération à travers un partenariat de firmes. Il existe une vaste littérature sur les effets économiques de la coopération entre les firmes des différentes phases de la chaîne de valeur. Au moins en termes économiques, ceci semble être un problème bien compris. La situation est différente pour ce qui est de la coopération entre les firmes concurrentes. Les stratégies peuvent être considérées comme un mélange de réduction de coûts, différentiation de produits et amélioration de la prise de décision et/ou du planning. Dans ce contexte, la technologie de l'information peut aider une firme à créer des avantages compétitifs soutenus sur les concurrents. Il est moins clair si la coopération est d'une quelconque utilité dans un tel environnement. Selon la littérature économique, les facteurs les plus importants affectant les bénéfices de la coopération sont la structure du marché, la forme et le degré d'incertitude à laquelle font face les firmes, leurs préférences pour le risque et le(s) type(s) de produit(s) offert(s) - produits homogènes ou hétérogènes. Les résultats rapportés dépendent de la manière dont ces facteurs sont combinés. Ils se contredisent en partie les uns les autres. Dans ce travail, l'auteur analyse le cas le plus intéressant d'un oligopole avec des produits différenciés, une incertitude de la demande et des managers averses aux risques. Cette combinaison n'a pas encore été analysée en détail, bien que ce soit le cas le plus réaliste. L'auteur présente un modèle micro-économique et utilise pour l'analyse des techniques de la théorie des jeux. La manière dont le modèle est construit permettra la dérivation de solutions de forme fermée (closed-form solutions). On obtiendra des résultats indiquant si la coopération dans différents domaines a du sens ou non. Ceci permet de juger le potentiel de la coopération technologique disponible. Le modèle simple présenté peut être étendu de différentes manières et être ainsi mieux adapté à la réalité. Kredit und Kapital 2/2004 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.37.2.202 | Generated on 2023-01-16 13:21:00