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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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    File URL: http://dept.econ.yorku.ca/research/workingPapers/working_papers/2007/CorrelatedNashEquilibrium2007.pdf
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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.
    2. Antoine Billot & Alain Chateauneuf & Itzhak Gilboa & Jean-Marc Tallon, 2000. "Sharing Beliefs: Between Agreeing and Disagreeing," Econometrica, Econometric Society, vol. 68(3), pages 685-694, May.
    3. Robert Aumann & Adam Brandenburger, 2014. "Epistemic Conditions for Nash Equilibrium," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 5, pages 113-136 World Scientific Publishing Co. Pte. Ltd..
    4. Joseph Greenberg, 2000. "The Right to Remain Silent," Theory and Decision, Springer, vol. 48(2), pages 193-204, March.
    5. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    6. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    7. Lo, Kin Chung, 1999. "Extensive Form Games with Uncertainty Averse Players," Games and Economic Behavior, Elsevier, vol. 28(2), pages 256-270, August.
    8. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
    9. Lawrence Blume & Adam Brandenburger & Eddie Dekel, 2014. "Lexicographic Probabilities and Choice Under Uncertainty," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 6, pages 137-160 World Scientific Publishing Co. Pte. Ltd..
    10. Marinacci, Massimo, 2000. "Ambiguous Games," Games and Economic Behavior, Elsevier, vol. 31(2), pages 191-219, May.
    11. Dow James & Werlang Sergio Ribeiro Da Costa, 1994. "Nash Equilibrium under Knightian Uncertainty: Breaking Down Backward Induction," Journal of Economic Theory, Elsevier, vol. 64(2), pages 305-324, December.
    12. Ben Polak, 1999. "Epistemic Conditions for Nash Equilibrium, and Common Knowledge of Rationality," Econometrica, Econometric Society, vol. 67(3), pages 673-676, May.
    13. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    14. Lo, Kin Chung, 2006. "Agreement and stochastic independence of belief functions," Mathematical Social Sciences, Elsevier, vol. 51(1), pages 1-22, January.
    15. Larry G. Epstein, 1999. "A Definition of Uncertainty Aversion," Review of Economic Studies, Oxford University Press, vol. 66(3), pages 579-608.
    16. 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.
    17. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    18. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, May.
    19. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February.
    20. 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.
    21. 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.
    22. Robert J Aumann, 1999. "Agreeing to Disagree," Levine's Working Paper Archive 512, David K. Levine.
    23. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-780, July.
    24. Lo, Kin Chung, 2007. "Sharing beliefs about actions," Mathematical Social Sciences, Elsevier, vol. 53(2), pages 123-133, March.
    25. Lo, Kin Chung, 2000. "A note on mutually absolutely continuous belief systems," Economics Letters, Elsevier, vol. 68(2), pages 149-156, August.
    26. Epstein, Larry G., 1997. "Preference, Rationalizability and Equilibrium," Journal of Economic Theory, Elsevier, vol. 73(1), pages 1-29, March.
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    Citations

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    Cited by:

    1. Frank Riedel & Linda Sass, 2014. "Ellsberg games," Theory and Decision, Springer, vol. 76(4), pages 469-509, April.
    2. 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.
    3. Calford, Evan, 2016. "Mixed Strategies in Games with Ambiguity Averse Agents," MPRA Paper 74909, University Library of Munich, Germany.
    4. Stauber, Ronald, 2017. "Irrationality and ambiguity in extensive games," Games and Economic Behavior, Elsevier, vol. 102(C), pages 409-432.
    5. Evan Calford, 2017. "Uncertainty Aversion in Game Theory: Experimental Evidence," Purdue University Economics Working Papers 1291, Purdue University, Department of Economics.
    6. 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.

    More about this item

    Keywords

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

    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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