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A Note on Kuhn's Theorem with Ambiguity Averse Players

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  • Gaurab Aryal
  • Ronald Stauber

Abstract

Kuhn's Theorem shows that extensive games with perfect recall can equivalently be analyzed using mixed or behavioral strategies, as long as players are expected utility maximizers. This note constructs an example that illustrate the limits of Kuhn's Theorem in an environment with ambiguity averse players who use maxmin decision rule and full Bayesian updating.

Suggested Citation

  • Gaurab Aryal & Ronald Stauber, 2014. "A Note on Kuhn's Theorem with Ambiguity Averse Players," Papers 1408.1022, arXiv.org, revised Aug 2014.
    • Handle: RePEc:arx:papers:1408.1022
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    References listed on IDEAS

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    1. Sass, Linda, 2014. "Kuhn's Theorem for Extensive Form Ellsberg Games," Center for Mathematical Economics Working Papers 478, Center for Mathematical Economics, Bielefeld University.
    2. Aryal, Gaurab & Stauber, Ronald, 2014. "A note on Kuhn’s Theorem with ambiguity averse players," Economics Letters, Elsevier, vol. 125(1), pages 110-114.
    3. Frank Riedel & Linda Sass, 2014. "Ellsberg games," Theory and Decision, Springer, vol. 76(4), pages 469-509, April.
    4. Atsushi Kajii & Takashi Ui, 2005. "Incomplete Information Games With Multiple Priors," The Japanese Economic Review, Japanese Economic Association, vol. 56(3), pages 332-351, September.
    5. Epstein Larry G. & Le Breton Michel, 1993. "Dynamically Consistent Beliefs Must Be Bayesian," Journal of Economic Theory, Elsevier, vol. 61(1), pages 1-22, October.
    6. Muraviev, Igor & Riedel, Frank & Sass, Linda, 2017. "Kuhn’s Theorem for extensive form Ellsberg games," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 26-41.
    7. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    8. Lo, Kin Chung, 1996. "Equilibrium in Beliefs under Uncertainty," Journal of Economic Theory, Elsevier, vol. 71(2), pages 443-484, November.
    9. R. H. Strotz, 1955. "Myopia and Inconsistency in Dynamic Utility Maximization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(3), pages 165-180.
    10. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    11. Gaurab Aryal & Ronald Stauber, 2014. "Trembles in extensive games with ambiguity averse players," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(1), pages 1-40, September.
    12. Maschler,Michael & Solan,Eilon & Zamir,Shmuel, 2013. "Game Theory," Cambridge Books, Cambridge University Press, number 9781107005488.
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    Citations

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    Cited by:

    1. Aryal, Gaurab & Stauber, Ronald, 2014. "A note on Kuhn’s Theorem with ambiguity averse players," Economics Letters, Elsevier, vol. 125(1), pages 110-114.
    2. Frank Riedel, 2017. "Uncertain Acts in Games," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 34(4), pages 275-292, December.
    3. Gaurab Aryal & Dong-Hyuk Kim, 2013. "Emprical Relevance of Ambiguity in First Price Auction Models," ANU Working Papers in Economics and Econometrics 2013-607, Australian National University, College of Business and Economics, School of Economics.
    4. Muraviev, Igor & Riedel, Frank & Sass, Linda, 2017. "Kuhn’s Theorem for extensive form Ellsberg games," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 26-41.
    5. Pahlke, Marieke, 2022. "Dynamic consistency in incomplete information games with multiple priors," Games and Economic Behavior, Elsevier, vol. 133(C), pages 85-108.
    6. Bauch, Gerrit & Riedel, Frank, 2024. "The Texas Shoot-Out under Knightian uncertainty," Games and Economic Behavior, Elsevier, vol. 146(C), pages 35-50.
    7. Gaurab Aryal & Ronald Stauber, 2014. "Trembles in extensive games with ambiguity averse players," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(1), pages 1-40, September.
    8. Gerrit Bauch & Frank Riedel, 2022. "The Texas Shootout under Uncertainty," Papers 2211.10089, arXiv.org.
    9. Gerrit Bauch, 2023. "Underreaction and dynamic inconsistency in communication games under noise," Papers 2311.12496, arXiv.org.
    10. Stauber, Ronald, 2017. "Irrationality and ambiguity in extensive games," Games and Economic Behavior, Elsevier, vol. 102(C), pages 409-432.

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    More about this item

    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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