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Purification and disambiguation of Ellsberg equilibria

Author

Listed:
  • Benoit Decerf

    (University of Namur)

  • Frank Riedel

    (Bielefeld University
    University of Johannesburg)

Abstract

Recently, the use of Knightian (uncertain) strategies in normal form games has received increasing attention. The use of uncertain acts in games leads to new (Ellsberg) equilibria. We provide a foundation of the new equilibrium concept in the spirit of Harsanyi by proving an extension of the Purification Theorem for $$2\times 2$$2×2 normal form games. Our result implies that Ellsberg equilibria are limits of equilibria in slightly perturbed games with private information. In such equilibria, players use pure or maxmin strategies only.

Suggested Citation

  • Benoit Decerf & Frank Riedel, 2020. "Purification and disambiguation of Ellsberg equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(3), pages 595-636, April.
  • Handle: RePEc:spr:joecth:v:69:y:2020:i:3:d:10.1007_s00199-019-01186-8
    DOI: 10.1007/s00199-019-01186-8
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    References listed on IDEAS

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    1. Bade, Sophie, 2011. "Ambiguous act equilibria," Games and Economic Behavior, Elsevier, vol. 71(2), pages 246-260, March.
    2. 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.
    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. Subir Bose & Ludovic Renou, 2014. "Mechanism Design With Ambiguous Communication Devices," Econometrica, Econometric Society, vol. 82(5), pages 1853-1872, September.
    5. Jacob K. Goeree & Charles A. Holt, 2001. "Ten Little Treasures of Game Theory and Ten Intuitive Contradictions," American Economic Review, American Economic Association, vol. 91(5), pages 1402-1422, December.
    6. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    7. Joseph Greenberg, 2000. "The Right to Remain Silent," Theory and Decision, Springer, vol. 48(2), pages 193-204, March.
    8. Alfredo Di Tillio & Nenad Kos & Matthias Messner, 2012. "The Design of Ambiguous Mechanisms," Working Papers 446, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    9. 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.
    10. repec:oup:restud:v:84:y::i:1:p:237-276. is not listed on IDEAS
    11. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February.
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    More about this item

    Keywords

    Knightian uncertainty; Ellsberg games; Ambiguity aversion; Purification; Disambiguation;
    All these keywords.

    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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