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Equilibrium in Beliefs Under Uncertainty

  • Kin Chung Lo

Existing equilibrium concepts for games make use of the subjective expected utility model axiomatized by Savage (1954) to represent players' preferences. Accordingly, each player's beliefs about the strategies played by opponents are represented by a probability measure. Motivated by experimental findings such as the Ellsberg Paradox demonstrating that the beliefs of a decision maker may not be representable by a probability measure, this paper generalizes equilibrium concepts for normal form games to allow for the beliefs of each player to be representable by a closed and convex set of probability measures. The implications of this generalization for the strategy choices and welfare of players are studied.

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File URL: https://www.economics.utoronto.ca/public/workingPapers/UT-ECIPA-ECPAP-95-02.ps
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File URL: https://www.economics.utoronto.ca/public/workingPapers/UT-ECIPA-ECPAP-95-02.pdf
File Function: Main Text
Download Restriction: no

Paper provided by University of Toronto, Department of Economics in its series Working Papers with number ecpap-95-02.

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Length: 41 pages
Date of creation: 11 Mar 1995
Date of revision:
Handle: RePEc:tor:tecipa:ecpap-95-02
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  1. 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.
  2. Mark J. Machina & David Schmeidler, 1990. "A More Robust Definition of Subjective Probability," Discussion Paper Serie A 306, University of Bonn, Germany.
  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. Uzi Segal, 1989. "Two-Stage Lotteries Without the Reduction Axiom," UCLA Economics Working Papers 552, UCLA Department of Economics.
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  7. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
  8. D. Pearce, 2010. "Rationalizable Strategic Behavior and the Problem of Perfection," Levine's Working Paper Archive 523, David K. Levine.
  9. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
  10. Dekel, Eddie & Safra, Zvi & Segal, Uzi, 1991. "Existence and dynamic consistency of Nash equilibrium with non-expected utility preferences," Journal of Economic Theory, Elsevier, vol. 55(2), pages 229-246, December.
  11. Camerer, Colin & Weber, Martin, 1992. " Recent Developments in Modeling Preferences: Uncertainty and Ambiguity," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 325-70, October.
  12. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
  13. Tan, Tommy Chin-Chiu & da Costa Werlang, Sergio Ribeiro, 1988. "The Bayesian foundations of solution concepts of games," Journal of Economic Theory, Elsevier, vol. 45(2), pages 370-391, August.
  14. Machina, Mark J, 1989. "Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1622-68, December.
  15. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, June.
  16. Adam Brandenburger, 1992. "Knowledge and Equilibrium in Games," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 83-101, Fall.
  17. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  18. Dow, James & Werlang, Sergio Ribeiro da Costa, 1992. "Uncertainty Aversion, Risk Aversion, and the Optimal Choice of Portfolio," Econometrica, Econometric Society, vol. 60(1), pages 197-204, January.
  19. Crawford, Vincent P., 1990. "Equilibrium without independence," Journal of Economic Theory, Elsevier, vol. 50(1), pages 127-154, February.
  20. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March.
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