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Rationalizability in continuous games

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  • Arieli, Itai

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).

Suggested Citation

  • Arieli, Itai, 2010. "Rationalizability in continuous games," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 912-924, September.
  • Handle: RePEc:eee:mateco:v:46:y:2010:i:5:p:912-924
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    References listed on IDEAS

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    1. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    2. Friedenberg, Amanda, 2010. "When do type structures contain all hierarchies of beliefs?," Games and Economic Behavior, Elsevier, vol. 68(1), pages 108-129, January.
    3. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    4. D. Pearce, 2010. "Rationalizable Strategic Behavior and the Problem of Perfection," Levine's Working Paper Archive 523, David K. Levine.
    5. Apt Krzysztof R., 2007. "The Many Faces of Rationalizability," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 7(1), pages 1-39, May.
    6. Adam Brandenburger & Eddie Dekel, 2014. "Hierarchies of Beliefs and Common Knowledge," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 2, pages 31-41 World Scientific Publishing Co. Pte. Ltd..
    7. Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
    8. Adam Brandenburger & Amanda Friedenberg, 2014. "Intrinsic Correlation in Games," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 4, pages 59-111 World Scientific Publishing Co. Pte. Ltd..
    9. 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.
    10. Battigalli Pierpaolo & Siniscalchi Marciano, 2003. "Rationalization and Incomplete Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 3(1), pages 1-46, June.
    11. Adam Brandenburger & Eddie Dekel, 2014. "Rationalizability and Correlated Equilibria," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 3, pages 43-57 World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Yi-Chun Chen & Xiao Luo & Chen Qu, 2016. "Rationalizability in general situations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 147-167, January.
    2. repec:eee:gamebe:v:106:y:2017:i:c:p:75-88 is not listed on IDEAS
    3. Haomiao Yu, 2014. "Rationalizability in large games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(2), pages 457-479, February.
    4. repec:eee:mateco:v:72:y:2017:i:c:p:82-87 is not listed on IDEAS
    5. Yi-Chun Chen & Xiao Luo & Chen Qu, 2016. "Rationalizability in general situations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 147-167, January.

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    Keywords

    Rationalizability Continuous games;

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