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

  • Reny, Phil
  • Robson, Arthur

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 Vancouver School of Economics in its series working papers with number robson-04-02-12-12-44-46.

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Length: 0 pages
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. 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.
  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. 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.
  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.
  5. Matsui, Akihiko, 1989. "Information leakage forces cooperation," Games and Economic Behavior, Elsevier, vol. 1(1), pages 94-115, March.
  6. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
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