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On the elimination of dominated strategies in stochastic models of evolution with large populations

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  • Kuzmics, Christoph

Abstract

A stochastic myopic best-reply dynamics is said to have property (W), for a given number of players n, if every pure weakly dominated strategy in every n-player game is eliminated in the long-run distribution of play induced by the dynamics. In this paper I give a necessary and sufficient condition that a dynamics has to satisfy in order for it to have property (W). The key determinant is found to be the sensitivity of the learning-rate to small payoff differences, inherent in the dynamics. If this sensitivity is higher than a certain cut-off, which depends on the number of players, then the dynamics satisfies property (W). If it is equal to or below that cut-off, then the dynamics does not satisfy property (W).

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 72 (2011)
Issue (Month): 2 (June)
Pages: 452-466

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Handle: RePEc:eee:gamebe:v:72:y:2011:i:2:p:452-466

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Web page: http://www.elsevier.com/locate/inca/622836

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Keywords: Learning Experimentation S[infinity]W-procedure Weak dominance Iterated strict dominance;

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  1. 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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  5. Hart, Sergiu, 2002. "Evolutionary dynamics and backward induction," Games and Economic Behavior, Elsevier, vol. 41(2), pages 227-264, November.
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  8. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  9. Ritzberger, Klaus, 2002. "Foundations of Non-Cooperative Game Theory," OUP Catalogue, Oxford University Press, number 9780199247868, September.
  10. Kuzmics, Christoph, 2004. "Stochastic evolutionary stability in extensive form games of perfect information," Games and Economic Behavior, Elsevier, vol. 48(2), pages 321-336, August.
  11. Samuelson Larry, 1994. "Stochastic Stability in Games with Alternative Best Replies," Journal of Economic Theory, Elsevier, vol. 64(1), pages 35-65, October.
  12. Gul, Faruk, 1996. "Rationality and Coherent Theories of Strategic Behavior," Journal of Economic Theory, Elsevier, vol. 70(1), pages 1-31, July.
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