IDEAS home Printed from https://ideas.repec.org/p/tor/tecipa/ecpap-95-04.html
   My bibliography  Save this paper

Nash Equilibrium without Mutual Knowledge of Rationality

Author

Listed:
  • Kin Chung Lo

Abstract

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.

Suggested Citation

  • Kin Chung Lo, 1995. "Nash Equilibrium without Mutual Knowledge of Rationality," Working Papers ecpap-95-04, University of Toronto, Department of Economics.
  • Handle: RePEc:tor:tecipa:ecpap-95-04
    as

    Download full text from publisher

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

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

    Other versions of this item:

    References listed on IDEAS

    as
    1. Crawford, Vincent P., 1990. "Equilibrium without independence," Journal of Economic Theory, Elsevier, vol. 50(1), pages 127-154, February.
    2. 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..
    3. 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..
    4. 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.
    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. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Equilibrium Refinements," Econometrica, Econometric Society, vol. 59(1), pages 81-98, January.
    7. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    8. 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.
    9. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lo, Kin Chung, 2009. "Correlated Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 144(2), pages 722-743, March.
    2. 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.
    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. Lo, Kin Chung, 2002. "Correlated equilibrium under uncertainty," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 183-209, November.
    6. repec:ebl:ecbull:v:4:y:2006:i:37:p:1-7 is not listed on IDEAS
    7. Lo, Kin Chung, 2011. "Possibility and permissibility," Mathematical Social Sciences, Elsevier, vol. 62(2), pages 109-113, September.
    8. Epstein, Larry G., 1997. "Preference, Rationalizability and Equilibrium," Journal of Economic Theory, Elsevier, vol. 73(1), pages 1-29, March.
    9. Marie Goppelsroeder & Maarten Pieter Schinkel & Jan Tuinstra, 2008. "QUANTIFYING THE SCOPE FOR EFFICIENCY DEFENSE IN MERGER CONTROL: THE WERDEN-FROEB-INDEX -super-," Journal of Industrial Economics, Wiley Blackwell, vol. 56(4), pages 778-808, December.
    10. Kin Chung Lo, 1998. "Epistemic Conditions for Agreement and Stochastic Independence of epsilon-Contaminated Beliefs," Working Papers 1998_02, York University, Department of Economics.
    11. 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, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    12. Lo, Kin Chung, 2005. "More likely than unlikely," Mathematical Social Sciences, Elsevier, vol. 49(1), pages 39-53, January.
    13. 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

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tor:tecipa:ecpap-95-04. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (RePEc Maintainer). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.