Bayesian Inference for Quantal Response Equilibrium in Normal-Form Games

Abstract

This paper develops a framework for estimating Quantal Response Equilibrium models from experimental data using Bayesian techniques. Bayesian techniques offer some advantages over the more commonly-used maximum likelihood approach: (i) the accuracy of the posterior simulation is limited by (increasingly plentiful) computational resources, both in hardware and software, rather than the validity of an asymptotic assumption that may not be reasonable with typical experimental sample sizes; (ii) Bayesian hierarchical models are a useful way to organize heterogeneity in one's data; and (iii) Bayesian inference allows us to test whether Quantal Response Equilibrium better organizes data than does (say) Nash equilibrium or purely random behavior, without rigging the test in favor of one of these by calling it the null hypothesis. As Quantal Response Equilibrium is a non-linear model, I also discuss some issues with choosing appropriate priors. Namely, choosing a very flat prior for the choice precision parameter implies a prior on choice probabilities with too much mass near Nash equilibrium and/or random choice. I propose a prior calibration process which seeks to avoid this problem by targeting the implied prior distribution of equilibrium choice probabilities.