Chapter 60 Quantal Response Equilibria: A Brief Synopsis

The quantal response equilibrium (QRE) is an extension of the standard model of Nash equilibrium which allows for errors in choice. The QRE can be viewed as a generalization of statistical models of discrete choice behavior of individuals to a game theoretic setting. Just like in discrete choice models of individual behavior, individuals are assumed to have an observed and unobserved component of their utility function. However, unlike in models of individual choice, the unobserved part of an individual's utility is unobserved not just to the econometrician, but also to the other players in the game. Thus, the game becomes a game of incomplete information. A QRE is simply a Bayesian equilibrium to this game. In a QRE, individuals do not choose the strategy with the highest (observed) utility for sure, but rather choose it with a probability that is a function of the utility difference between that strategy and other strategies.