Reinterpreting Mixed Strategy Equilibria: A Unification of the Classical and Bayesian Views
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.
|Date of creation:||12 Feb 2004|
|Date of revision:||12 Feb 2004|
|Contact details of provider:|| Web page: http://www.economics.ubc.ca/|
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.:
- 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..
- Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, vol. 63(5), pages 1161-1180, September.
- 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.
- Werlang, Sérgio Ribeiro da Costa & Chin-Chiu Tan, Tommy, 1987. "The Bayesian Foundations of solution concepts of games," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 111, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
- 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.
- Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
- Robert J. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Working Paper Archive 661465000000000377, David K. Levine.
- R. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Bibliography 513, UCLA Department of Economics.
- Matsui, Akihiko, 1989. "Information leakage forces cooperation," Games and Economic Behavior, Elsevier, vol. 1(1), pages 94-115, March.
- Akihiko Matsui, 1988. "Information Leakage Forces Cooperation," Discussion Papers 786, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- 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.
- Robson, A.J., 1990. "An "Informationally Robust Equilibrium" For Two-Person Nonzero-Sum Games," Papers 9039, Tilburg - Center for Economic Research.
- Robson, A.J., 1990. "An "informationally robust equilibrium" for two-person nonzero-sum games," Discussion Paper 1990-39, Tilburg University, Center for Economic Research.