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Nash equilibrium without mutual knowledge of rationality

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  • Kin Chung Lo

    (Department of Economics, York University, Toronto, Ontario, M3J 1P3 CANADA)

Abstract

In a Nash equilibrium, players' rationality is mutual knowledge. However, both intuition and experimental evidence suggest that players do not know for sure the rationality of opponents. This paper proposes a new equilibrium concept, cautious equilibrium, that generalizes Nash equilibrium in terms of preferences in two person strategic games. In a cautious equilibrium, players do not necessarily know the rationality of opponents, but they view rationality as infinitely more likely than irrationality. For suitable models of preference, cautious equilibrium predicts that a player might take a "cautious" strategy that is not a best response in any Nash equilibrium.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joecth:v:14:y:1999:i:3:p:621-633
    Note: Received: January 28, 1998; revised version October 2, 1998
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    References listed on IDEAS

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    1. Crawford, Vincent P., 1990. "Equilibrium without independence," Journal of Economic Theory, Elsevier, vol. 50(1), pages 127-154, February.
    2. 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..
    3. 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.
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    5. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    6. 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.
    7. 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..
    8. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Equilibrium Refinements," Econometrica, Econometric Society, vol. 59(1), pages 81-98, January.
    9. 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.
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    Citations

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    Cited by:

    1. Emiliano Catonini & Nicodemo De Vito, 2023. "Cautious Belief and Iterated Admissibility," Papers 2305.15330, arXiv.org.
    2. Konstantin Fursov & Thomas Thurner, 2016. "God Helps Those Who Help Themselves! A Study of User-Innovation in Russia," HSE Working papers WP BRP 59/STI/2016, National Research University Higher School of Economics.
    3. Burkhard C. Schipper, 2021. "The evolutionary stability of optimism, pessimism, and complete ignorance," Theory and Decision, Springer, vol. 90(3), pages 417-454, May.
    4. Werlang, Sérgio Ribeiro da Costa, 2000. "A notion of subgame perfect Nash equilibrium under knightian uncertainty," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 376, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    5. Marie Goppelsroeder & Maarten Pieter Schinkel & Jan Tuinstra, 2008. "Quantifying The Scope For Efficiency Defense In Merger Control: The Werden‐Froeb‐Index," Journal of Industrial Economics, Wiley Blackwell, vol. 56(4), pages 778-808, December.
    6. Lo, Kin Chung, 2009. "Correlated Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 144(2), pages 722-743, March.
    7. Jürgen Eichberger & David Kelsey, 2011. "Are the treasures of game theory ambiguous?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 313-339, October.
    8. Lo, Kin Chung, 2002. "Correlated equilibrium under uncertainty," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 183-209, November.
    9. repec:ebl:ecbull:v:4:y:2006:i:37:p:1-7 is not listed on IDEAS
    10. Lo, Kin Chung, 2011. "Possibility and permissibility," Mathematical Social Sciences, Elsevier, vol. 62(2), pages 109-113, September.
    11. Jürgen Eichberger & David Kelsey & Burkhard Schipper, 2008. "Granny Versus Game Theorist: Ambiguity in Experimental Games," Theory and Decision, Springer, vol. 64(2), pages 333-362, March.
    12. Lo, Kin Chung, 1999. "Extensive Form Games with Uncertainty Averse Players," Games and Economic Behavior, Elsevier, vol. 28(2), pages 256-270, August.
    13. Eichberger, Jurgen & Kelsey, David, 2002. "Strategic Complements, Substitutes, and Ambiguity: The Implications for Public Goods," Journal of Economic Theory, Elsevier, vol. 106(2), pages 436-466, October.
    14. Lo, Kin Chung, 2005. "More likely than unlikely," Mathematical Social Sciences, Elsevier, vol. 49(1), pages 39-53, January.
    15. Catonini, Emiliano & De Vito, Nicodemo, 2020. "Weak belief and permissibility," Games and Economic Behavior, Elsevier, vol. 120(C), pages 154-179.
    16. Jürgen Eichberger & David Kelsey & Burkhard Schipper, 2008. "Granny Versus Game Theorist: Ambiguity in Experimental Games," Theory and Decision, Springer, vol. 64(2), pages 333-362, March.
    17. Catonini, Emiliano, 2019. "Rationalizability and epistemic priority orderings," Games and Economic Behavior, Elsevier, vol. 114(C), pages 101-117.
    18. Epstein, Larry G., 1997. "Preference, Rationalizability and Equilibrium," Journal of Economic Theory, Elsevier, vol. 73(1), pages 1-29, March.
    19. Kin Chung Lo, 1998. "Epistemic Conditions for Agreement and Stochastic Independence of epsilon-Contaminated Beliefs," Working Papers 1998_02, York University, Department of Economics.
    20. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February.

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    More about this item

    Keywords

    Nash equilibrium; Cautious equilibrium; Mutual knowledge of rationality.;
    All these keywords.

    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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