Stochastic game theory for social science: a primer on quantal response equilibrium

Abstract

Quantal response equilibrium replaces the sharp best responses of standard game theory with smoothed “quantal” responses. This theory incorporates elements of stochastic choice originally developed by mathematical psychologists and statisticians into an equilibrium in which players’ beliefs that motivate decisions are consistent with the stochastic choices resulting from those decisions. This paper provides an introduction to quantal response models, with intuitive graphical representations that highlight connections to Nash equilibrium and level-k analysis in non-cooperative games. The analysis clarifies how standard (i.i.d.) error assumptions provide sharp, falsifiable predictions, even without specific distributional assumptions (logit, probit, etc.).The emphasis is on a coherent behavioral game theory that explains intuitive deviations from Nash equilibrium predictions in experimental games. This primer walks the reader through a series of examples illustrating the application of QRE theory to simple matrix games, multiplayer games, games with continuous strategy spaces, multistage games in extensive form, and Bayesian games.