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Kuhn’s Theorem for extensive form Ellsberg games

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  • Muraviev, Igor
  • Riedel, Frank
  • Sass, Linda

Abstract

We propose the notions of mixed and behavioral Ellsberg strategies for extensive form games and prove that these strategies are outcome-equivalent if and only if mixed Ellsberg strategies satisfy a certain rectangularity condition. In addition, we show that not only the profile of Ellsberg strategies must be appropriately chosen but also the extensive form must satisfy further restrictions beyond those implied by perfect recall in order to ensure that each player will respect his ex ante strategy choice with the evolution of play.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:mateco:v:68:y:2017:i:c:p:26-41
    DOI: 10.1016/j.jmateco.2016.11.004
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    Cited by:

    1. Jürgen Eichberger & Simon Grant & David Kelsey, 2017. "Ambiguity and the Centipede Game: Strategic Uncertainty in Multi-Stage Games," Discussion Papers 1705, University of Exeter, Department of Economics.
    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, 2017. "Uncertain Acts in Games," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 34(4), pages 275-292, December.
    4. Pahlke, Marieke, 2022. "Dynamic consistency in incomplete information games with multiple priors," Games and Economic Behavior, Elsevier, vol. 133(C), pages 85-108.
    5. 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.
    6. 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.
    7. Stauber, Ronald, 2017. "Irrationality and ambiguity in extensive games," Games and Economic Behavior, Elsevier, vol. 102(C), pages 409-432.
    8. 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.
    9. Dorian Beauchêne, 2016. "Solution concepts for games with ambiguous payoffs," Theory and Decision, Springer, vol. 80(2), pages 245-269, February.
    10. 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.
    11. 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.
    12. Grant, Simon & Meneghel, Idione & Tourky, Rabee, 2016. "Savage games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    13. Gerrit Bauch, 2023. "Underreaction and dynamic inconsistency in communication games under noise," Papers 2311.12496, arXiv.org.
    14. 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.
    15. Pahlke, Marieke, 2022. "Dynamic Consistency and Ambiguous Communication," VfS Annual Conference 2022 (Basel): Big Data in Economics 264027, Verein für Socialpolitik / German Economic Association.

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