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Reinterpreting Mixed Strategy Equilibria: A Unification of the Classical and Bayesian Views

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Reny, Phil
Robson, Arthur

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Abstract

We provide a new interpretation of mixed strategy equilibria that incorporates both von Neumann and Morgenstern's classical concealment role of mixing as well as the more recent Bayesian view originating with Harsanyi. For any two-person game, G, we consider an incomplete information game, IG, in which each player's type is the probability he assigns to the event that his mixed strategy in G is 'found out' by his opponent. We show that, generically, any regular equilibrium of G can be approximated by an equilibrium of IG in which almost every type of each player is strictly optimizing. This leads us to interpret i's equilibrium mixed strategy in G as a combination of deliberate randomization by i together with uncertainty on j's part about which randomization i will employ. We also show that such randomization is not unusual: For example, i's randomization is nondegenerate whenever the support of an equilibrium contains cyclic best replies.

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Paper provided by Microeconomics.ca Website in its series Micro Theory Working Papers with number robson-04-02-12-12-44-46.

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Date of creation: 12 Feb 2004
Date of revision: 12 Feb 2004
Handle: RePEc:ubc:pmicro:robson-04-02-12-12-44-46

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  1. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January. [Downloadable!] (restricted)
  2. Reny, Philip J. & Robson, Arthur J., 2004. "Reinterpreting mixed strategy equilibria: a unification of the classical and Bayesian views," Games and Economic Behavior, Elsevier, vol. 48(2), pages 355-384, August. [Downloadable!] (restricted)
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  3. Matsui, Akihiko, 1989. "Information leakage forces cooperation," Games and Economic Behavior, Elsevier, vol. 1(1), pages 94-115, March. [Downloadable!] (restricted)
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  4. Tan, Tommy Chin-Chiu & da Costa Werlang, Sergio Ribeiro, 1988. "The Bayesian foundations of solution concepts of games," Journal of Economic Theory, Elsevier, vol. 45(2), pages 370-391, August. [Downloadable!] (restricted)
  5. Robson~ Arthur J., 1994. "An Informationally Robust Equilibrium for Two-Person Nonzero-Sum Games," Games and Economic Behavior, Elsevier, vol. 7(2), pages 233-245, September. [Downloadable!] (restricted)
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  6. Rosenthal, Robert W., 1991. "A note on robustness of equilibria with respect to commitment opportunities," Games and Economic Behavior, Elsevier, vol. 3(2), pages 237-243, May. [Downloadable!] (restricted)
  7. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, vol. 63(5), pages 1161-80, September. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Robin Cubitt & Robert Sugden, 2005. "Common reasoning in games: a resolution of the paradoxes of ‘common knowledge of rationality’," Discussion Papers 2005-17, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham. [Downloadable!]
  2. Stephen Morris, 2006. "Purification," Levine's Bibliography 321307000000000470, UCLA Department of Economics. [Downloadable!]
  3. Hans Reijnierse & Peter Borm & Mark Voorneveld, 2007. "On ‘Informationally Robust Equilibria’ for Bimatrix Games," Economic Theory, Springer, vol. 30(3), pages 539-560, March. [Downloadable!] (restricted)
  4. Reny, Phil & Robson, Arthur, 2004. "Reinterpreting Mixed Strategy Equilibria: A Unification of the Classical and Bayesian Views," Micro Theory Working Papers robson-04-02-12-12-44-46, Microeconomics.ca Website, revised 12 Feb 2004. [Downloadable!]
    Other versions:
  5. Gallice, Andrea, 2007. "Best Responding to What? A Behavioral Approach to One Shot Play in 2x2 Games," Discussion Papers in Economics 1365, University of Munich, Department of Economics. [Downloadable!]
  6. Xiao Luo & Yi-Chun Chen, 2004. "A Unified Approach to Information, Knowledge, and Stability," Econometric Society 2004 Far Eastern Meetings 472, Econometric Society. [Downloadable!]
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