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Kuhn's Theorem for Extensive Form Ellsberg Games

Author

Listed:
  • Mouraviev, Igor

    (Center for Mathematical Economics, Bielefeld University)

  • Riedel, Frank

    (Center for Mathematical Economics, Bielefeld University)

  • Sass, Linda

    (Center for Mathematical Economics, Bielefeld University)

Abstract

The paper generalizes Kuhn's Theorem to extensive form games in which players condition their play on the realization of ambiguous randomization devices and use a maxmin decision rule to evaluate the consequences of their decisions. It proves that ambiguous behavioral and ambiguous mixed strate- gies are payoff-and outcome equivalent only if the latter strategies satisfy a rectangularity condition. The paper also discusses dynamic consistency. In particular, it shows that not only the profile of ambiguous strategies must be appropriately chosen but also the extensive form must satisfy further re- strictions beyond those implied by perfect recall in order to ensure that each player respects her ex ante contingent choice with the evolution of play.

Suggested Citation

  • Mouraviev, Igor & Riedel, Frank & Sass, Linda, 2016. "Kuhn's Theorem for Extensive Form Ellsberg Games," Center for Mathematical Economics Working Papers 510, Center for Mathematical Economics, Bielefeld University.
  • Handle: RePEc:bie:wpaper:510
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    References listed on IDEAS

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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. Pahlke, Marieke, 2022. "Dynamic Consistency and Ambiguous Communication," VfS Annual Conference 2022 (Basel): Big Data in Economics 264027, Verein für Socialpolitik / German Economic Association.
    4. Eichberger, Jürgen & Grant, Simon & Kelsey, David, 2017. "Ambiguity and the Centipede Game: Strategic Uncertainty in Multi-Stage Games," Working Papers 0638, University of Heidelberg, Department of Economics.
    5. Eran Hanany & Peter Klibanoff & Sujoy Mukerji, 2020. "Incomplete Information Games with Ambiguity Averse Players," American Economic Journal: Microeconomics, American Economic Association, vol. 12(2), pages 135-187, May.
    6. Pahlke, Marieke, 2022. "Dynamic consistency in incomplete information games with multiple priors," Games and Economic Behavior, Elsevier, vol. 133(C), pages 85-108.
    7. Gerrit Bauch, 2023. "Underreaction and dynamic inconsistency in communication games under noise," Papers 2311.12496, arXiv.org.
    8. 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.
    9. Battigalli, P. & Catonini, E. & Lanzani, G. & Marinacci, M., 2019. "Ambiguity attitudes and self-confirming equilibrium in sequential games," Games and Economic Behavior, Elsevier, vol. 115(C), pages 1-29.
    10. Stauber, Ronald, 2017. "Irrationality and ambiguity in extensive games," Games and Economic Behavior, Elsevier, vol. 102(C), pages 409-432.
    11. Dorian Beauchêne, 2016. "Solution concepts for games with ambiguous payoffs," Theory and Decision, Springer, vol. 80(2), pages 245-269, February.
    12. 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.
    13. Pahlke, Marieke, 2018. "Dynamic Consistency in Incomplete Information Games with Multiple Priors," Center for Mathematical Economics Working Papers 599, Center for Mathematical Economics, Bielefeld University.
    14. Grant, Simon & Meneghel, Idione & Tourky, Rabee, 2016. "Savage games," Theoretical Economics, Econometric Society, vol. 11(2), May.

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    Keywords

    Kuhn's Theorem; Strategic Ambiguity; Maxmin Utility; Ellsberg Games;
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