Quantal Response Equilibria for Normal Form Games

Abstract

We investigate the use of standard statistical models for quantal choice in a game theoretic setting. Players choose strategies based on relative expected utility, and assume other players do so as well. We define a Quantal Response Equilibrium (QRE) as a fixed point of this process, and establish existence. For a logit specification of the error structure, we show that as the error goes to zero, QRE approaches a subset of Nash equilibria and also implies a unique selection from the set of Nash equilibria in generic games. We fit the model to a variety of experimental data sets by using maximum likelihood estimatation. JEL Classification numbers: C19, C44, C72, C92 QUANTAL RESPONSE EQUILIBRIA FOR NORMAL FORM GAMES Richard D. McKelvey Thomas R. Palfrey 1 Introduction We investigate the possibility of using standard statistical models for quantal choice in a game theoretic setting. Players choose among strategies in the normal form of a game based on their relative expected utilit...