A myopic adjustment process leading to best-reply matching

We analyze a myopic strategy adjustment process in strategic-form games. It is shown that the steady states of the continuous time limit, which is constructed assuming frequent play and slow adjustment of strategies, are exactly the best-reply matching equilibria, as discussed by Droste, Kosfeld, and Voorneveld (2000. Mimeo, Tilburg University). In a best-reply matching equilibrium every player ?matches' the probability of playing a pure strategy to the probability that this pure strategy is a best reply to the pure-strategy profile played by his opponents. We derive stability results for the steady states of the continuous time limit in 2×2 bimatrix games and coordination games. Analyzing the asymptotic behavior of the stochastic adjustment process in discrete time shows convergence to minimal curb sets of the game. Moreover, absorbing states of the process correspond to best-reply matching equilibria of the game. A Myopic Adjustment Process Leading to Best-Reply Matching∗ Michael Kosfeld† Institute for Empirical Research in Economics University of Zurich Blümlisalpstrasse 10 CH-8006 Zurich Switzerland Edward Droste KPMG Economic Consulting P.O. Box 559 NL-2130 AN Hoofddorp The Netherlands Mark Voorneveld‡ Department of Economics Stockholm School of Economics Box 6501 SE-113 83 Stockholm Sweden ∗Published in: Games and Economic Behavior 40, 2002, 270-298. We would like to thank Eric van Damme, Urs Fischbacher, Bill Sandholm, Dolf Talman, and an anonymous referee for useful comments and suggestions. We are particularly grateful to Josef Hofbauer for many helpful comments and for pointing us to a general convergence result in two-player games. The result is included in the appendix of the paper. †This author’s research has been financially supported by the European Commission through a Marie Curie Fellowship at CentER for Economic Research, Tilburg University. ‡Part of this author’s research was financially supported by the Dutch Foundation for Mathematical Research (SWON) through project 613-04-051. Proposed Running Head: Adjustment to Best-Reply Matching Corresponding author: Michael Kosfeld Institute for Empirical Research in Economics University of Zurich Blümlisalpstrasse 10 CH-8006 Zurich Switzerland phone: +41 1 634 3761 fax: +41 1 634 4907 email: [email protected] Abstract We analyze a myopic strategy adjustment process in strategic-form games. It is shown that the steady states of the continuous time limit, which is constructed assuming frequent play and slow adjustment of strategies, are exactly the best-reply matching equilibria, as discussed in Droste et al. (2000). In a best-reply matching equilibrium every player ‘matches’ the probability of playing a pure strategy to the probability that this pure strategy is a best reply to the pure strategy profile played by his opponents. We derive stability results for the steady states of the continuous time limit in 2×2 bimatrix games and coordination games. Analyzing the asymptotic behavior of the stochastic adjustment process in discrete time shows convergence to minimal curb sets of the game. Moreover, absorbing states of the process correspond to best-reply matching equilibria of the game. Journal of Economic Literature Classification Numbers: C72, D83.We analyze a myopic strategy adjustment process in strategic-form games. It is shown that the steady states of the continuous time limit, which is constructed assuming frequent play and slow adjustment of strategies, are exactly the best-reply matching equilibria, as discussed in Droste et al. (2000). In a best-reply matching equilibrium every player ‘matches’ the probability of playing a pure strategy to the probability that this pure strategy is a best reply to the pure strategy profile played by his opponents. We derive stability results for the steady states of the continuous time limit in 2×2 bimatrix games and coordination games. Analyzing the asymptotic behavior of the stochastic adjustment process in discrete time shows convergence to minimal curb sets of the game. Moreover, absorbing states of the process correspond to best-reply matching equilibria of the game. Journal of Economic Literature Classification Numbers: C72, D83.