A Statistical Theory of Equilibrium in Games
This paper describes a statistical model of equilibrium behavior in games, which we call Quanta! Response Equilibrium (QRE). The key feature of the equilibrium is that individuals do not always play best responses to the strategies of their opponents, but play better strategies with higher probability than worse strategies. We illustrate several different applications of this approach, and establish a number of theoretical properties of this equilibrium concept. We also demonstrate an equivalence between this equilibrium notion and Bayesian games derived from games of complete information with perturbed payoffs.
We acknowledge support of National Science Foundation Grant No. SBR-9223701 to the California Institute of Technology and the support of the JPL-Caltech supercomputer project. A version of this paper was presented at the First Japanese Decentralization Conference at Keio University in November, 1994. We are grateful to the warm hospitality during that conference, and appreciate the comments received from the audience. The second author thanks the Laboratoire d'Economie Industrielle and CERAS for research support and hospitality. We acknowledge valuable discussions with Mahmoud El-Gamal, Jacques-François Thisse, and Mark Fey, and the research assistance of Eugene Grayver and Rob Weber. Published as McKelvey, Richard D., and Thomas R. Palfrey. "A statistical theory of equilibrium in games." The Japanese Economic Review 47, no. 2 (1996): 186-209.
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