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Epistemic Conditions for Nash Equilibrium


  • Aumann, Robert
  • Brandenburger, Adam


Sufficient conditions for Nash equilibrium in an 'n'-person game are given in terms of what the players know and believe - about the game, and about each other's rationality, actions, knowledge, and beliefs. Mixed strategies are treated not as conscious randomizations, but as conjectures, on the part of other players, as to what a player will do. Common knowledge plays a smaller role in characterizing Nash equilibrium than had been supposed. When 'n' = 2, mutual knowledge of the payoff functions, of rationality, and of the conjectures implies that the conjectures form a Nash equilibrium. When 'n [greater than or equal to] 3 and there is a common prior, mutual knowledge of the payoff functions and of rationality, and common knowledge of the conjectures, imply that the conjectures form a Nash equilibrium. Examples show the results to be tight. Copyright 1995 by The Econometric Society.

Suggested Citation

  • Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, vol. 63(5), pages 1161-1180, September.
  • Handle: RePEc:ecm:emetrp:v:63:y:1995:i:5:p:1161-80

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    References listed on IDEAS

    1. Jeongwen Chiang, 1991. "A Simultaneous Approach to the Whether, What and How Much to Buy Questions," Marketing Science, INFORMS, vol. 10(4), pages 297-315.
    2. Tülin Erdem & Susumu Imai & Michael Keane, 2003. "Brand and Quantity Choice Dynamics Under Price Uncertainty," Quantitative Marketing and Economics (QME), Springer, vol. 1(1), pages 5-64, March.
    3. Victor Aguirregabiria, 1999. "The Dynamics of Markups and Inventories in Retailing Firms," Review of Economic Studies, Oxford University Press, vol. 66(2), pages 275-308.
    4. Boizot, Christine & Robin, Jean-Marc & Visser, Michael, 2001. "The Demand for Food Products: An Analysis of Interpurchase Times and Purchased Quantities," Economic Journal, Royal Economic Society, vol. 111(470), pages 391-419, April.
    5. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    6. Hugo Benitez-Silva & John Rust & Gunter Hitsch & Giorgio Pauletto & George Hall, 2000. "A Comparison Of Discrete And Parametric Methods For Continuous-State Dynamic Programming Problems," Computing in Economics and Finance 2000 24, Society for Computational Economics.
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    8. Aguirregabiria, Victor, 2005. "Nonparametric identification of behavioral responses to counterfactual policy interventions in dynamic discrete decision processes," Economics Letters, Elsevier, vol. 87(3), pages 393-398, June.
    9. Boztuğ, Yasemin & Bell, David R., 2004. "The Effect of Inventory on Purchase Incidence: Empirical Analysis of Opposing Forces of Storage and Consumption," Papers 2004,43, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
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    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games


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