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Rationalizability in continuous games

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  • Arieli, Itai
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    Abstract

    Define a continuous game to be one in which every player's strategy set is a Polish space, and the payoff function of each player is bounded and continuous. We prove that in this class of games the process of sequentially eliminating "never-best-reply" strategies terminates before or at the first uncountable ordinal, and this bound is tight. Also, we examine the connection between this process and common belief of rationality in the universal type space of Mertens and Zamir (1985).

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Mathematical Economics.

    Volume (Year): 46 (2010)
    Issue (Month): 5 (September)
    Pages: 912-924

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    Handle: RePEc:eee:mateco:v:46:y:2010:i:5:p:912-924

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    Web page: http://www.elsevier.com/locate/jmateco

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    Keywords: Rationalizability Continuous games;

    References

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    1. Eddie Dekel & Drew Fudenberg & Stephen Morris, 2006. "Interim Correlated Rationalizability," Levine's Bibliography 122247000000001188, UCLA Department of Economics.
    2. D. Pearce, 2010. "Rationalizable Strategic Behavior and the Problem of Perfection," Levine's Working Paper Archive 523, David K. Levine.
    3. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February.
    4. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 514, David K. Levine.
    5. P. Battigalli & M. Siniscalchi, 2002. "Rationalization and Incomplete Information," Princeton Economic Theory Working Papers, David K. Levine 9817a118e65062903de7c3577, David K. Levine.
    6. Friedenberg, Amanda, 2010. "When do type structures contain all hierarchies of beliefs?," Games and Economic Behavior, Elsevier, vol. 68(1), pages 108-129, January.
    7. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, Econometric Society, vol. 55(6), pages 1391-1402, November.
    8. Lipman Barton L., 1994. "A Note on the Implications of Common Knowledge of Rationality," Games and Economic Behavior, Elsevier, vol. 6(1), pages 114-129, January.
    9. Brandenburger, Adam & Friedenberg, Amanda, 2008. "Intrinsic correlation in games," Journal of Economic Theory, Elsevier, vol. 141(1), pages 28-67, July.
    10. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, Econometric Society, vol. 52(4), pages 1029-50, July.
    11. Apt Krzysztof R., 2007. "The Many Faces of Rationalizability," The B.E. Journal of Theoretical Economics, De Gruyter, De Gruyter, vol. 7(1), pages 1-39, May.
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    Cited by:
    1. Haomiao Yu, 2014. "Rationalizability in large games," Economic Theory, Springer, Springer, vol. 55(2), pages 457-479, February.

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