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Nash Equilibrium without Mutual Knowledge of Rationality

  • Kin Chung Lo

This paper defines an equilibrium concept for general preferences in two person normal form games. It collapses to Nash Equilibrium when preferences are represented by the expected utility model. An important characteristic of the equilibrium concept is that player i does not necessarily know that player j is rational, but she views rationality as infinitely more likely than irrationality. For suitable models of preferences, the equilibrium concept predicts that a player will take a "cautious" strategy that is not a best response in any Nash Equilibrium.

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File URL: https://www.economics.utoronto.ca/public/workingPapers/UT-ECIPA-ECPAP-95-04.ps
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File URL: https://www.economics.utoronto.ca/public/workingPapers/UT-ECIPA-ECPAP-95-04.pdf
File Function: MainText
Download Restriction: no

Paper provided by University of Toronto, Department of Economics in its series Working Papers with number ecpap-95-04.

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Length: 17 pages
Date of creation: 09 Jul 1995
Date of revision:
Handle: RePEc:tor:tecipa:ecpap-95-04
Contact details of provider: Postal: 150 St. George Street, Toronto, Ontario
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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. Mukerji, S., 1995. "A theory of play for games in strategic form when rationality is not common knowledge," Discussion Paper Series In Economics And Econometrics 9519, Economics Division, School of Social Sciences, University of Southampton.
  3. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  4. 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.
  5. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, vol. 63(5), pages 1161-80, September.
  6. 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..
  7. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Equilibrium Refinements," Econometrica, Econometric Society, vol. 59(1), pages 81-98, January.
  8. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  9. Crawford, Vincent P., 1990. "Equilibrium without independence," Journal of Economic Theory, Elsevier, vol. 50(1), pages 127-154, February.
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