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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).

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  • 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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    Cited by:

    1. 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.
    2. Müller, Christoph, 2020. "Robust implementation in weakly perfect Bayesian strategies," Journal of Economic Theory, Elsevier, vol. 189(C).
    3. Pierpaolo Battigalli & Pietro Tebaldi, 2019. "Interactive epistemology in simple dynamic games with a continuum of strategies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(3), pages 737-763, October.
    4. Amanda Friedenberg & H. Jerome Keisler, 2021. "Iterated dominance revisited," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(2), pages 377-421, September.
    5. Weinstein, Jonathan & Yildiz, Muhamet, 2017. "Interim correlated rationalizability in infinite games," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 82-87.
    6. Seel, Christian & Tsakas, Elias, 2017. "Rationalizability and Nash equilibria in guessing games," Games and Economic Behavior, Elsevier, vol. 106(C), pages 75-88.
    7. Ritesh Jain & Michele Lombardi, 2022. "On Interim Rationalizable Monotonicity," Working Papers 202315, University of Liverpool, Department of Economics.
    8. Ritesh Jain and & Michele Lombardi, 2022. "Interim Rationalizable (and Bayes-Nash) Implementation of Functions: A full Characterization," CSEF Working Papers 645, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    9. 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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    Rationalizability Continuous games;

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