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Evolutionary stability in finite stopping games under a fast best-reply dynamics

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  • Zibo Xu

Abstract

We consider a fast evolutionary dynamic process on finite stopping games, where each player at each node has at most one move to continue the game. A state is evolutionarily stable if its long-run relative frequency of occurrence is bounded away from zero as the mutation rate decreases to zero. The fast dynamic process allows each individual in each population to change its strategy at every stage. We define a robustness index of backward induction and show examples where the backward induction equilibrium component is not evolutionarily stable for large populations. We show some sufficient conditions for evolutionary stability, which are different from the ones for the conventional evolutionary model. Even for this fast dynamic process, the transition between any two Nash equilibrium components may take very long time.

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  • Zibo Xu, 2013. "Evolutionary stability in finite stopping games under a fast best-reply dynamics," Discussion Paper Series dp632, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp632
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    1. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    2. Hart, Sergiu, 2002. "Evolutionary dynamics and backward induction," Games and Economic Behavior, Elsevier, vol. 41(2), pages 227-264, November.
    3. Ziv Gorodeisky, 2006. "Evolutionary Stability for Large Populations and Backward Induction," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 369-380, May.
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