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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.

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File URL: http://dept.econ.yorku.ca/research/workingPapers/working_papers/2007/CorrelatedNashEquilibrium2007.pdf
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Bibliographic Info

Paper provided by York University, Department of Economics in its series Working Papers with number 2007_5.

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Length: 24 pages
Date of creation: Sep 2007
Date of revision:
Handle: RePEc:yca:wpaper:2007_5

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

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References

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  1. Kin Chung Lo, 1995. "Equilibrium in Beliefs Under Uncertainty," Working Papers ecpap-95-02, University of Toronto, Department of Economics.
  2. Robert J. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Working Paper Archive 661465000000000377, David K. Levine.
  3. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
  4. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
  5. Kin Chung Lo, 1995. "Nash Equilibrium without Mutual Knowledge of Rationality," Working Papers ecpap-95-04, University of Toronto, Department of Economics.
  6. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, vol. 63(5), pages 1161-80, September.
  7. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-80, July.
  8. Dow, James & Werlang, Sérgio Ribeiro da Costa, 1992. "Nash equilibrium under knightian uncertainty: breaking-down backward induction," Economics Working Papers (Ensaios Economicos da EPGE) 186, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  9. repec:hal:cesptp:halshs-00174553 is not listed on IDEAS
  10. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February.
  11. Billot, A. & Chateauneuf, A. & Gilboa, I. & Tallon, J.-M., 1998. "Sharing Beliefs: Between Agreeing and Disagreeing," Papiers d'Economie Mathématique et Applications 98.30, Université Panthéon-Sorbonne (Paris 1).
  12. Lo, Kin Chung, 2000. "A note on mutually absolutely continuous belief systems," Economics Letters, Elsevier, vol. 68(2), pages 149-156, August.
  13. Ben Polak, 1999. "Epistemic Conditions for Nash Equilibrium, and Common Knowledge of Rationality," Econometrica, Econometric Society, vol. 67(3), pages 673-676, May.
  14. Epstein, Larry G., 1997. "Preference, Rationalizability and Equilibrium," Journal of Economic Theory, Elsevier, vol. 73(1), pages 1-29, March.
  15. Kin Chung Lo, 1995. "Extensive Form Games with Uncertainty Averse Players," Working Papers ecpap-95-03, University of Toronto, Department of Economics.
  16. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  17. Joseph Greenberg, 2000. "The Right to Remain Silent," Theory and Decision, Springer, vol. 48(2), pages 193-204, March.
  18. 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.
  19. Matthew J. Ryan, 2002. "What do uncertainty-averse decision-makers believe?," Economic Theory, Springer, vol. 20(1), pages 47-65.
  20. Lo, Kin Chung, 2007. "Sharing beliefs about actions," Mathematical Social Sciences, Elsevier, vol. 53(2), pages 123-133, March.
  21. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Choice under Uncertainty," Econometrica, Econometric Society, vol. 59(1), pages 61-79, January.
  22. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  23. Epstein, Larry G, 1999. "A Definition of Uncertainty Aversion," Review of Economic Studies, Wiley Blackwell, vol. 66(3), pages 579-608, July.
  24. Lo, Kin Chung, 2006. "Agreement and stochastic independence of belief functions," Mathematical Social Sciences, Elsevier, vol. 51(1), pages 1-22, January.
  25. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
  26. Marinacci, Massimo, 2000. "Ambiguous Games," Games and Economic Behavior, Elsevier, vol. 31(2), pages 191-219, May.
  27. Robert J Aumann, 1999. "Agreeing to Disagree," Levine's Working Paper Archive 512, David K. Levine.
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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.

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