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Correlated Nash Equilibrium

  • Kin Chung Lo

    ()

    (Department of Economics, York University)

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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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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  1. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  2. Lo, Kin Chung, 2006. "Agreement and stochastic independence of belief functions," Mathematical Social Sciences, Elsevier, vol. 51(1), pages 1-22, January.
  3. Kin Chung Lo, 1995. "Nash Equilibrium without Mutual Knowledge of Rationality," Working Papers ecpap-95-04, University of Toronto, Department of Economics.
  4. Lo, Kin Chung, 1996. "Equilibrium in Beliefs under Uncertainty," Journal of Economic Theory, Elsevier, vol. 71(2), pages 443-484, November.
  5. 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.
  6. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, June.
  7. Epstein, Larry G, 1999. "A Definition of Uncertainty Aversion," Review of Economic Studies, Wiley Blackwell, vol. 66(3), pages 579-608, July.
  8. Lo, Kin Chung, 1999. "Extensive Form Games with Uncertainty Averse Players," Games and Economic Behavior, Elsevier, vol. 28(2), pages 256-270, August.
  9. 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.
  10. Joseph Greenberg, 2000. "The Right to Remain Silent," Theory and Decision, Springer, vol. 48(2), pages 193-204, March.
  11. R. Aumann, 2010. "Subjectivity and Correlation in Randomized Strategies," Levine's Working Paper Archive 389, David K. Levine.
  12. Mark J. Machina & David Schmeidler, 1990. "A More Robust Definition of Subjective Probability," Discussion Paper Serie A 306, University of Bonn, Germany.
  13. Robert J. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Working Paper Archive 661465000000000377, David K. Levine.
  14. Epstein, Larry G., 1997. "Preference, Rationalizability and Equilibrium," Journal of Economic Theory, Elsevier, vol. 73(1), pages 1-29, March.
  15. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Choice under Uncertainty," Econometrica, Econometric Society, vol. 59(1), pages 61-79, January.
  16. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February.
  17. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
  18. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  19. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, vol. 63(5), pages 1161-80, September.
  20. 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.
  21. Ben Polak, 1999. "Epistemic Conditions for Nash Equilibrium, and Common Knowledge of Rationality," Econometrica, Econometric Society, vol. 67(3), pages 673-676, May.
  22. Matthew J. Ryan, 2002. "What do uncertainty-averse decision-makers believe?," Economic Theory, Springer, vol. 20(1), pages 47-65.
  23. Robert J Aumann, 1999. "Agreeing to Disagree," Levine's Working Paper Archive 512, David K. Levine.
  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. Marinacci, Massimo, 2000. "Ambiguous Games," Games and Economic Behavior, Elsevier, vol. 31(2), pages 191-219, May.
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