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Correlated Nash Equilibrium

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  • Kin Chung Lo

    (Department of Economics, York University)

Abstract

Nash equilibrium presumes that players have expected utility preferences, and therefore the beliefs of each player are represented by a probability measure. Motivated by Ellsberg-type behavior, which contradicts the probabilistic representation of beliefs, we generalize Nash equilibrium in n-player strategic games to allow for preferences conforming to the maxmin expected utility model of Gilboa and Schmeidler [Journal of Mathematical Economics, 18 (1989), 141–153]. With no strings attached, our equilibrium concept can be characterized by the suitably modified epistemic conditions for Nash equilibrium.

Suggested Citation

  • Kin Chung Lo, 2007. "Correlated Nash Equilibrium," Working Papers 2007_5, York University, Department of Economics.
    • Handle: RePEc:yca:wpaper:2007_5
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    References listed on IDEAS

    as
    1. Lo, Kin Chung, 1996. "Equilibrium in Beliefs under Uncertainty," Journal of Economic Theory, Elsevier, vol. 71(2), pages 443-484, November.
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    22. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February.
    23. Kin Chung Lo, 1999. "Nash equilibrium without mutual knowledge of rationality," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(3), pages 621-633.
    24. Matthew J. Ryan, 2002. "What do uncertainty-averse decision-makers believe?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(1), pages 47-65.
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    27. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-780, July.
    28. Lo, Kin Chung, 2007. "Sharing beliefs about actions," Mathematical Social Sciences, Elsevier, vol. 53(2), pages 123-133, March.
    29. Lo, Kin Chung, 2000. "A note on mutually absolutely continuous belief systems," Economics Letters, Elsevier, vol. 68(2), pages 149-156, August.
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    Cited by:

    1. Calford, Evan, 2016. "Mixed Strategies in Games with Ambiguity Averse Agents," MPRA Paper 74909, University Library of Munich, Germany.
    2. Stauber, Ronald, 2017. "Irrationality and ambiguity in extensive games," Games and Economic Behavior, Elsevier, vol. 102(C), pages 409-432.
    3. Calford, Evan M., 2020. "Uncertainty aversion in game theory: Experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 176(C), pages 720-734.
    4. Leonardo Pejsachowicz, 2016. "Stochastic Independence under Knightian Uncertainty," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01753323, HAL.
    5. Calford, Evan M., 2021. "Mixed strategies and preference for randomization in games with ambiguity averse agents," Journal of Economic Theory, Elsevier, vol. 197(C).
    6. Frank Riedel & Linda Sass, 2014. "Ellsberg games," Theory and Decision, Springer, vol. 76(4), pages 469-509, April.
    7. Lang, Matthias & Wambach, Achim, 2013. "The fog of fraud – Mitigating fraud by strategic ambiguity," Games and Economic Behavior, Elsevier, vol. 81(C), pages 255-275.
    8. Evan M. Calford & Gregory DeAngelo, 2023. "Ambiguity and enforcement," Experimental Economics, Springer;Economic Science Association, vol. 26(2), pages 304-338, April.
    9. Dominiak, Adam & Eichberger, Jürgen, 2021. "Games in context: Equilibrium under ambiguity for belief functions," Games and Economic Behavior, Elsevier, vol. 128(C), pages 125-159.
    10. Leonardo Pejsachowicz, 2016. "Stochastic Independence under Knightian Uncertainty," Post-Print hal-01753323, HAL.
    11. Azrieli, Yaron & Teper, Roee, 2011. "Uncertainty aversion and equilibrium existence in games with incomplete information," Games and Economic Behavior, Elsevier, vol. 73(2), pages 310-317.

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    More about this item

    Keywords

    Agreeing to disagree; Correlated equilibrium; Epistemic conditions; Knightian uncertainty; Multiple priors; Nash equilibrium;
    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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