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Nash equilibrium without mutual knowledge of rationality

Author

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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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    Cited by:

    1. 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.
    2. Catonini, Emiliano & De Vito, Nicodemo, 2024. "Cautious belief and iterated admissibility," Journal of Mathematical Economics, Elsevier, vol. 110(C).
    3. Lo, Kin Chung, 1999. "Extensive Form Games with Uncertainty Averse Players," Games and Economic Behavior, Elsevier, vol. 28(2), pages 256-270, August.
    4. 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.
    5. Keisler, H. Jerome & Lee, Byung Soo, 2023. "Common assumption of rationality," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    6. 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.
    7. Burkhard C. Schipper, 2021. "The evolutionary stability of optimism, pessimism, and complete ignorance," Theory and Decision, Springer, vol. 90(3), pages 417-454, May.
    8. 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.
    9. 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).
    10. Lo, Kin Chung, 2005. "More likely than unlikely," Mathematical Social Sciences, Elsevier, vol. 49(1), pages 39-53, January.
    11. Catonini, Emiliano & De Vito, Nicodemo, 2020. "Weak belief and permissibility," Games and Economic Behavior, Elsevier, vol. 120(C), pages 154-179.
    12. 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.
    13. Lo, Kin Chung, 2002. "Correlated equilibrium under uncertainty," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 183-209, November.
    14. repec:ebl:ecbull:v:4:y:2006:i:37:p:1-7 is not listed on IDEAS
    15. Catonini, Emiliano, 2019. "Rationalizability and epistemic priority orderings," Games and Economic Behavior, Elsevier, vol. 114(C), pages 101-117.
    16. Lo, Kin Chung, 2011. "Possibility and permissibility," Mathematical Social Sciences, Elsevier, vol. 62(2), pages 109-113, September.
    17. Lo, Kin Chung, 2009. "Correlated Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 144(2), pages 722-743, March.
    18. 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.
    19. Epstein, Larry G., 1997. "Preference, Rationalizability and Equilibrium," Journal of Economic Theory, Elsevier, vol. 73(1), pages 1-29, March.
    20. Kin Chung Lo, 1998. "Epistemic Conditions for Agreement and Stochastic Independence of epsilon-Contaminated Beliefs," Working Papers 1998_02, York University, Department of Economics.
    21. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February.

    More about this item

    Keywords

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    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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