بازی با مکمل های راهبردی: برنامه های کاربردی جدید برای سازمان های صنعتی

This paper provides an introduction to the analysis of games with strategic complementarities and applications to industrial organization: oligopoly pricing, comparative statics and a taxonomy of strategic behavior in two-stage games.

Games of strategic complementarities are those in which the best response of any player is increasing in actions of the rivals. Many games usually studied in industrial organization display strategic complementarities including a large subset of those involving search, network externalities, oligopoly interaction, or patent races. Recently, there has been a surge of interest in the study of competition in the presence of complementarities in industries with a network component, such as credit cards, or where systems competition is important, like in software. Supermodular games (Topkis, 1979, Vives, 1985a, Vives, 1990 and Milgrom and Roberts, 1990) provide the appropriate framework to model strategic interaction in the presence of complementarities. The theory of supermodular games is based on a lattice-theoretic approach that exploits order and monotonicity properties. Both existence of equilibrium and comparative static properties are based on order and monotonicity properties in contrast to the usual box of tools based on convex analysis and calculus. The approach is powerful and delivers strong results. In the class of supermodular games the existence of equilibrium in pure strategies is ensured without requiring quasiconcavity of payoffs; the equilibrium set has an order structure, having extremal elements that allows a global analysis of the set; there is an algorithm to compute extremal equilibria, which also bound the rationalizable set; and monotone comparative statics results are obtained with minimal assumptions. The purpose of the paper is to provide an introduction to the class of supermodular games and provide some applications in industrial organization analysis. We obtain new results and new light is cast on old results by getting rid of unnecessary assumptions. In this way the role of the critical assumptions is highlighted. At the same time the range of application of the theory is extended beyond games of strategic complementarities, providing examples of results obtained in games displaying strategic substitutability. The reader is warned however that the approach, although useful in a very large class of cases, is not of universal applicability.

In this paper I have surveyed briefly the theory and some applications to industrial organization of supermodular games. The survey has not been, by any means, exhaustive. For example, dynamics have only been considered in the simple format of two-stage games in Section 4. However, full-fledged dynamic games can be analyzed with the lattice-theoretic techniques. For example, Jun and Vives (2004) and Sleet (2001) analyze differential games, and Hoppe and Lehmann-Grube (2002) develop applications to innovation timing games. Cabral and Villas-Boas (2002) consider multimarket oligopoly applications and Anderson and Schmitt (2003) a quota game in international trade. Coordination failures in macroeconomics and financial markets as well as cumulative processes in the presence of complementarities and monopolistic competition provide more examples outside the realm of Industrial Organization.6 Bayesian games provide another fertile ground of applications of the method, advancing the frontier in auction theory and global games and equilibrium selection. See Vives, 1999 and Vives, in press for some of the mentioned extensions. Finally, recent work has tested for complementarities in innovation and organizational design using the tools presented in this article.7