SSE/EFI Working Paper Series in Economics and Finance
Stochastic Better-Reply Dynamics in Games
Abstract: In Young (1993, 1998) agents are recurrently matched to
play a finite game and almost always play a myopic best reply to a
frequency distribution based on a sample from the recent history of play.
He proves that in a generic class of finite n-player games, as the mutation
rate tends to zero, only strategies in certain minimal sets closed under
best replies will be played with positive probability. In this paper we
alter Young's behavioral assumption and allow agents to choose not only
best replies, but also better replies. The better-reply correspondence maps
distributions over the player's own and her opponents' strategies to those
pure strategies which gives the player at least the same expected payoff
against the distribution of her opponents' strategies. We prove that in
finite n-player games, the limiting distribution will put positive
probability only on strategies in certain minimal sets closed under better
replies. This result is consistent with and extends Ritzberger's and
Weibull's (1995) results on the equivalence of asymptotically stable
strategy-sets and closed sets under better replies in a deterministic
continuous-time model with sign-preserving selection dynamics.
Keywords: Evolutionary game theory; Markov chain; stochastic stability; better replies; (follow links to similar papers)
JEL-Codes: C72; C73; (follow links to similar papers)
19 pages, July 3, 2000
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