Quantal response equilibria with heterogeneous agents

This paper introduces a model of quantal response equilibrium with heterogeneous agents and demonstrates the existence of a representative agent for such populations. Except in rare cases, the representative agentʼs noise terms cannot be independently and identically distributed across the set of actions, even if that is assumed for the individual agents. This result demonstrates a fundamental difference between a representative agent and truly heterogeneous quantal responders and suggests that when fitting quantal response specifications to aggregate data from a population of subjects, the noise terms should be allowed to be jointly dependent across actions. Even though this introduces additional degrees of freedom, it makes the model well specified. The representative agent inherits a regular quantal response function from the actual agents, so this model does impose falsifiable restrictions.