Equilibrium Selection and the Rate of Convergence in Coordination Games with Simultaneous Play

Flavio M. Menezes, Paulo K. Monteiro and Akram Temimi
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Flavio M. Menezes: Australian National University
Paulo K. Monteiro: Institute of Economics, University of Copenhagen
Akram Temimi: University of Alabama

No 98-14, Discussion Papers from University of Copenhagen. Department of Economics

Abstract: We apply the dynamic stochastic framework proposed in the recent evolutionary literature to a class of coordination games played simultaneously by the entire population. In these games, payoffs whence best replies are determined by a summary statistic of the population strategy profile. We demonstrate that with simultaneous play, the equilibrium selection depends crucially on how best responses to the summary statistic remain piece-wise constant. In fact, all the strict Nash equilibria in the underlying stage game can be declared stochastically stable depending on how the best response mapping generates piece-wise constant best responses. Furthermore, we show that if the best response mapping is sufficiently asymmetric, the expected waiting time until the unique stochastically stable state is reached is of the same order as the mutation rate, even in the limit as the population size grows to infinity.

Keywords: equilibrium selection; stochastic stability; waiting time; rate of convergence (search for similar items in EconPapers)
JEL-codes: C72 C73 (search for similar items in EconPapers)
Pages: 29 pages
Date: 1998-08
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