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Trembles in Extensive Games with Ambiguity Averse Players

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  • Gaurab Aryal
  • Ronald Stauber

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Abstract

We introduce and analyze three definitions of equilibrium for finite extensive games with imperfect information and ambiguity averse players. In a setting where players' preferences are represented by maxmin expected utility as characterized in Gilboa and Schmeidler (1989), our definitions capture the intuition that players may consider the possibility of slight mistakes, analogous to the intuition leading to trembling-hand perfect equilibrium as introduced in Selten (1975). We prove existence for two of our equilibrium notions, and relate our definitions to standard equilibrium concepts with expected utility maximizing players. Our analysis shows that ambiguity aversion can lead to distinct behavioral implications, even if ambiguous beliefs only arise from the possibility of slight mistakes in the implementation of unambiguous strategies.

Suggested Citation

  • Gaurab Aryal & Ronald Stauber, 2013. "Trembles in Extensive Games with Ambiguity Averse Players," ANU Working Papers in Economics and Econometrics 2013-606, Australian National University, College of Business and Economics, School of Economics.
  • Handle: RePEc:acb:cbeeco:2013-606
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    File URL: https://www.cbe.anu.edu.au/researchpapers/econ/wp606.pdf
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    References listed on IDEAS

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    Cited by:

    1. Stauber, Ronald, 2017. "Irrationality and ambiguity in extensive games," Games and Economic Behavior, Elsevier, vol. 102(C), pages 409-432.
    2. Sass, Linda, 2014. "Kuhn's Theorem for Extensive Form Ellsberg Games," Center for Mathematical Economics Working Papers 478, Center for Mathematical Economics, Bielefeld University.
    3. Aryal, Gaurab & Stauber, Ronald, 2014. "A note on Kuhn’s Theorem with ambiguity averse players," Economics Letters, Elsevier, vol. 125(1), pages 110-114.
    4. de Castro, Luciano I. & Liu, Zhiwei & Yannelis, Nicholas C., 2017. "Implementation under ambiguity," Games and Economic Behavior, Elsevier, vol. 101(C), pages 20-33.
    5. Igor Kopylov, 2016. "Subjective probability, confidence, and Bayesian updating," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(4), pages 635-658, October.
    6. Luciano I. Castro & Zhiwei Liu & Nicholas C. Yannelis, 2017. "Ambiguous implementation: the partition model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 233-261, January.

    More about this item

    Keywords

    Extensive games; Ambiguity; Maxmin;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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