Stability and trembles in extensive-form games
AbstractA leading solution concept in the evolutionary study of extensive-form games is Selten's (1983) (selten1983evolutionary) notion of limit ESS. We demonstrate that a limit ESS does not imply neutral stability, and that it may be dynamically unstable (almost any small perturbation takes the population away). These problems arise due to an implicit assumption that “mutants” are arbitrarily rare relative to “trembling” incumbents. Finally, we present a novel definition that solves this issue and has appealing properties.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 48160.
Date of creation: 09 Jul 2013
Date of revision:
Limit ESS; evolutionary stability; extensive-form games.;
Find related papers by JEL classification:
- C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-08-05 (All new papers)
- NEP-EVO-2013-08-05 (Evolutionary Economics)
- NEP-GTH-2013-08-05 (Game Theory)
- NEP-HPE-2013-08-05 (History & Philosophy of Economics)
- NEP-MIC-2013-08-05 (Microeconomics)
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- Bomze Immanuel M. & Weibull Jorgen W., 1995. "Does Neutral Stability Imply Lyapunov Stability?," Games and Economic Behavior, Elsevier, vol. 11(2), pages 173-192, November.
- Bolton, Gary E., 1997. "The rationality of splitting equally," Journal of Economic Behavior & Organization, Elsevier, vol. 32(3), pages 365-381, March.
- Cressman, R., 1997. "Local stability of smooth selection dynamics for normal form games," Mathematical Social Sciences, Elsevier, vol. 34(1), pages 1-19, August.
- Sandholm, William H., 2010. "Local stability under evolutionary game dynamics," Theoretical Economics, Econometric Society, vol. 5(1), January.
- Bhaskar, V., 1998. "Noisy Communication and the Evolution of Cooperation," Journal of Economic Theory, Elsevier, vol. 82(1), pages 110-131, September.
- Bhaskar V., 1996.
"On the neutral stability of mixed strategies in asymmetric contests,"
Mathematical Social Sciences,
Elsevier, vol. 31(1), pages 56-57, February.
- Bhaskar, V., 1995. "On the neutral stability of mixed strategies in asymmetric contests," Mathematical Social Sciences, Elsevier, vol. 30(3), pages 273-284, December.
- Selten, Reinhard, 1983. "Evolutionary stability in extensive two-person games," Mathematical Social Sciences, Elsevier, vol. 5(3), pages 269-363, September.
- Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
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