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.|
|Contact details of provider:|| Postal: The Economic Research Institute, Stockholm School of Economics, P.O. Box 6501, 113 83 Stockholm, Sweden|
Phone: +46-(0)8-736 90 00
Fax: +46-(0)8-31 01 57
Web page: http://www.hhs.se/
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Hessel Oosterbeek & Randolph Sloof & Gijs van de Kuilen, 2004.
"Cultural differences in ultimatum game experiments: Evidence from a meta-analysis,"
- Hessel Oosterbeek & Randolph Sloof & Gijs van de Kuilen, 2004. "Cultural Differences in Ultimatum Game Experiments: Evidence from a Meta-Analysis," Experimental Economics, Springer;Economic Science Association, vol. 7(2), pages 171-188, 06.
- 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.
When requesting a correction, please mention this item's handle: RePEc:hhs:hastef:0743. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Helena Lundin)
If references are entirely missing, you can add them using this form.