Stochastic stability in finite extensive-form games of perfect information
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 stochastically stable.
|Date of creation:||21 Mar 2013|
|Date of revision:|
|Note:||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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- Sergiu Hart, 1999.
"Evolutionary Dynamics and Backward Induction,"
Game Theory and Information
9905002, EconWPA, revised 23 Mar 2000.
- Sergiu Hart & Andreu Mas-Colell, 2003. "Uncoupled Dynamics Do Not Lead to Nash Equilibrium," American Economic Review, American Economic Association, vol. 93(5), pages 1830-1836, December.
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- Hart, Sergiu, 1992. "Games in extensive and strategic forms," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 2, pages 19-40 Elsevier.
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