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Boundedly rational Nash equilibrium: a probabilistic choice approach

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  • CHEN, H.-C.
  • FRIEDMAN, J. W.
  • THISSE, J.-F.

Abstract

This paper proposes an equilibrium concept for n-person finite games based on boundedly rational decision making by players. The players are modeled as following random choice behavior in the manner of the logit model of discrete choice theory as set forth by Luce, McFadden and others. The behavior of other players determines in a natural way a lottery facing each player i. At equilibrium, each player is using the appropriate choice probabilities, given the choice probabilities used by the others in the game. The rationality of the players is parameterized on a continuum from complete rationality to uniform random choice. Using results by McKelvey and Palfrey, we show existence of an equilibrium for any finite n-person game and convergence to Nash equilibrium. We also identify conditions such that, for given rationality parameters the path of choices over time when the players use fictitious play (their beliefs about other players' choices are given by the empirical distributions of those players) converges to equilibrium.

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers RP with number -1248.

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Handle: RePEc:cor:louvrp:-1248

Note: In : Games and Economic Behavior, 18, 32-54, 1997
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  1. Victor Ginsburgh & André De Palma & Yorgo Papageorgiou & Jacques-François Thisse, 1999. "The principle of minimum differentiation holds under sufficient heterogeneity," ULB Institutional Repository 2013/3319, ULB -- Universite Libre de Bruxelles.
  2. Miyao, Takahiro & Shapiro, Perry, 1981. "Discrete Choice and Variable Returns to Scale," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(2), pages 257-73, June.
  3. Rosenthal, Robert W, 1989. "A Bounded-Rationality Approach to the Study of Noncooperative Games," International Journal of Game Theory, Springer, vol. 18(3), pages 273-91.
  4. Armen A. Alchian, 1950. "Uncertainty, Evolution, and Economic Theory," Journal of Political Economy, University of Chicago Press, vol. 58, pages 211.
  5. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
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