IDEAS home Printed from https://ideas.repec.org/p/bie/wpaper/478.html
   My bibliography  Save this paper

Kuhn's Theorem for Extensive Form Ellsberg Games

Author

Listed:
  • Sass, Linda

    (Center for Mathematical Economics, Bielefeld University)

Abstract

Riedel and Sass (2013) propose a framework for normal form games where players can use imprecise probabilistic devices. We extend this strategic use of objective ambiguity to extensive form games. We show that with rectangularity of Ellsberg strategies we have dynamic consistency in the sense of Kuhn (1953): rectangular Ellsberg strategies are equivalent to Ellsberg behavior strategies. We provide an example for our result and define Ellsberg equilibrium in such extensive form Ellsberg games.

Suggested Citation

  • Sass, Linda, 2014. "Kuhn's Theorem for Extensive Form Ellsberg Games," Center for Mathematical Economics Working Papers 478, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:478
    as

    Download full text from publisher

    File URL: https://pub.uni-bielefeld.de/download/2674088/2901849
    File Function: First Version, 2013
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Riedel, Frank, 2004. "Dynamic coherent risk measures," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 185-200, August.
    2. Rubinstein Ariel & Wolinsky Asher, 1994. "Rationalizable Conjectural Equilibrium: Between Nash and Rationalizability," Games and Economic Behavior, Elsevier, vol. 6(2), pages 299-311, March.
    3. Peter Klibanoff, 2001. "Stochastically independent randomization and uncertainty aversion," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(3), pages 605-620.
    4. Pierpaolo Battigalli & Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2015. "Self-Confirming Equilibrium and Model Uncertainty," American Economic Review, American Economic Association, vol. 105(2), pages 646-677, February.
    5. , & ,, 2007. "Updating preferences with multiple priors," Theoretical Economics, Econometric Society, vol. 2(3), September.
    6. Ebbe Groes & Hans Jørgen Jacobsen & Birgitte Sloth & Torben Tranaes, 1998. "Nash Equilibrium with Lower Probabilities," Theory and Decision, Springer, vol. 44(1), pages 37-66, January.
    7. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    8. David Kelsey & Willy Spanjers, 2004. "Ambiguity in Partnerships," Economic Journal, Royal Economic Society, vol. 114(497), pages 528-546, July.
    9. Joseph Greenberg, 2000. "The Right to Remain Silent," Theory and Decision, Springer, vol. 48(2), pages 193-204, March.
    10. Kalai, Ehud & Lehrer, Ehud, 1995. "Subjective games and equilibria," Games and Economic Behavior, Elsevier, vol. 8(1), pages 123-163.
    11. Gajdos, T. & Hayashi, T. & Tallon, J.-M. & Vergnaud, J.-C., 2008. "Attitude toward imprecise information," Journal of Economic Theory, Elsevier, vol. 140(1), pages 27-65, May.
    12. 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.
    13. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
    14. Lo, Kin Chung, 1999. "Extensive Form Games with Uncertainty Averse Players," Games and Economic Behavior, Elsevier, vol. 28(2), pages 256-270, August.
    15. Ma, Chenghu, 2000. "Uncertainty aversion and rationality in games of perfect information," Journal of Economic Dynamics and Control, Elsevier, vol. 24(3), pages 451-482, March.
    16. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Kellner, Christian & Le Quement, Mark T., 2017. "Modes of ambiguous communication," Games and Economic Behavior, Elsevier, vol. 104(C), pages 271-292.
    4. Stauber, Ronald, 2017. "Irrationality and ambiguity in extensive games," Games and Economic Behavior, Elsevier, vol. 102(C), pages 409-432.
    5. Dorian Beauchêne, 2016. "Solution concepts for games with ambiguous payoffs," Theory and Decision, Springer, vol. 80(2), pages 245-269, February.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Stauber, Ronald, 2017. "Irrationality and ambiguity in extensive games," Games and Economic Behavior, Elsevier, vol. 102(C), pages 409-432.
    3. Pahlke, Marieke, 2022. "Dynamic consistency in incomplete information games with multiple priors," Games and Economic Behavior, Elsevier, vol. 133(C), pages 85-108.
    4. Frank Riedel & Linda Sass, 2014. "Ellsberg games," Theory and Decision, Springer, vol. 76(4), pages 469-509, April.
    5. 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.
    6. 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.
    7. Riedel, Frank & Tallon, Jean-Marc & Vergopoulos, Vassili, 2018. "Dynamically consistent preferences under imprecise probabilistic information," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 117-124.
    8. Ellis, Andrew, 2018. "On dynamic consistency in ambiguous games," Games and Economic Behavior, Elsevier, vol. 111(C), pages 241-249.
    9. Lo, Kin Chung, 2009. "Correlated Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 144(2), pages 722-743, March.
    10. Hill, Brian, 2020. "Dynamic consistency and ambiguity: A reappraisal," Games and Economic Behavior, Elsevier, vol. 120(C), pages 289-310.
    11. 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.
    12. Bade, Sophie, 2022. "Dynamic semi-consistency," Games and Economic Behavior, Elsevier, vol. 134(C), pages 117-126.
    13. Federica Ceron & Vassili Vergopoulos, 2020. "Recursive objective and subjective multiple priors," Post-Print halshs-02900497, HAL.
    14. Agnieszka Wiszniewska-Matyszkiel, 2016. "Belief distorted Nash equilibria: introduction of a new kind of equilibrium in dynamic games with distorted information," Annals of Operations Research, Springer, vol. 243(1), pages 147-177, August.
    15. Federica Ceron & Vassili Vergopoulos, 2020. "Recursive objective and subjective multiple priors," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02900497, HAL.
    16. Battigalli, P. & Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M., 2016. "Analysis of information feedback and selfconfirming equilibrium," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 40-51.
    17. Federica Ceron & Vassili Vergopoulos, 2020. "Recursive objective and subjective multiple priors," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02563318, HAL.
    18. Sujoy Mukerji & Jean-Marc Tallon & EUREQua & CNRS - Universite Paris I., 2003. "An overview of economic applications of David Schmeidler`s models of decision making under uncertainty," Economics Series Working Papers 165, University of Oxford, Department of Economics.
    19. Li, Jian, 2020. "Preferences for partial information and ambiguity," Theoretical Economics, Econometric Society, vol. 15(3), July.
    20. Frank Riedel, 2017. "Uncertain Acts in Games," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 34(4), pages 275-292, December.

    More about this item

    Keywords

    Rectangularity; Kuhn's Theorem; Strategic Ambiguity; Extensive Form Ellsberg Games; Knightian Uncertainty in Games; Objective Ambiguity;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bie:wpaper:478. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Bettina Weingarten (email available below). General contact details of provider: https://edirc.repec.org/data/imbiede.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.