Homogeneity bias in models of discrete choice with bounded rationality

Quantal response equilibrium captures bounded rationality in a strategic game by adopting a stochastic model of discrete choice along with the traditional rational expectation framework. We examine the use of a single-agent, homogeneous parametric quantal response model (e.g., logit response) to describe the aggregate behavior of heterogeneous agents sharing the same parametric form for their quantal response functions, but having individual rationality parameters, in a symmetric population game. For any parametric quantal response function arising from a unimodal distribution of exchangeable payoff disturbances, we find that a mis-specified homogeneous rationality parameter will have downward bias. Logit response is one such specification. This result implies that empirical work that disregards heterogeneity underestimates subjects’ rationality.