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

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  • Reny, Phil
  • Robson, Arthur

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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Bibliographic Info

Paper provided by Vancouver School of Economics in its series Microeconomics.ca 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. 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.
  2. Robson, A.J., 1990. "An "informationally robust equilibrium" for two-person nonzero-sum games," Discussion Paper 1990-39, Tilburg University, Center for Economic Research.
  3. Akihiko Matsui, 1988. "Information Leakage Forces Cooperation," Discussion Papers 786, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
  5. 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.
  6. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, vol. 63(5), pages 1161-80, September.
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Cited by:
  1. Reijnierse, J.H. & Borm, P.E.M. & Voorneveld, M., 2007. "On 'informationally robust equilibria' for bimatrix games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-195638, Tilburg University.
  2. 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.
  3. von Stengel, Bernhard & Zamir, Shmuel, 2010. "Leadership games with convex strategy sets," Games and Economic Behavior, Elsevier, vol. 69(2), pages 446-457, July.
  4. Stephen Morris, 2006. "Purification," Levine's Bibliography 321307000000000470, UCLA Department of Economics.
  5. Xiao Luo & Yi-Chun Chen, 2004. "A Unified Approach to Information, Knowledge, and Stability," Econometric Society 2004 Far Eastern Meetings 472, Econometric Society.
  6. Bernhard von Stengel & Shmuel Zamir, 2010. "Leadership games with convex strategy sets," LSE Research Online Documents on Economics 27653, London School of Economics and Political Science, LSE Library.

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