SSE/EFI Working Paper Series in Economics and Finance
Stochastic stability in finite extensive-form games of perfect information
Abstract: We consider a basic stochastic evolutionary model with
rare mutation and a best-reply (or better-reply) selection mechanism.
Following Young's papers, we call a state stochastically stable if its
long-term relative frequency of occurrence is bounded away from zero as the
mutation rate decreases to zero. We prove that, for all finite
extensive-form games of perfect information, the best-reply dynamic
converges to a Nash equilibrium almost surely. Moreover, only Nash
equilibria can be stochastically stable. We present a `centipede-trust
game', where we prove that both the backward induction equilibrium
component and the Pareto-dominant equilibrium component are stochastically
stable, even when the populations increase to infinity. For finite
extensive-form games of perfect information, we give a sufficient condition
for stochastic stability of the set of non-backward-induction equilibria,
and show how much extra payoff is needed to turn an equilibrium
Keywords: Evolutionary game theory; Markov chains; equilibrium selection; stochastic stability; games in extensive form; games of perfect information; backward induction equilibrium; Nash equilibrium components; best-reply dynamics.; (follow links to similar papers)
JEL-Codes: C61; C62; C73; (follow links to similar papers)
60 pages, March 21, 2013
This working paper is a revised version of `Evolutionary stability in general extensive-form games of perfect information' in Discussion Paper Series 631, the Center for the Study of Rationality, Hebrew University of Jerusalem. The author is grateful to Sergiu Hart and Jorgen Weibull for many suggestions and discussions. The author also wishes to thank Katsuhiko Aiba, Tomas Rodriguez Barraquer, Yosef Rinott, Bill Sandholm and Eyal Winter for their comments. The author would like to acknowledge financial support from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement No. 249159, and from the Knut and Alice Wallenberg Foundation.
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