Heterogeneous Quantal Response Equilibrium and Cognitive Hierarchies

We explore an equilibrium model of games where players' choice behavior is given by logit response functions, but their payoff responsiveness and beliefs about other players' payoff responsiveness is heterogeneous. We extend the definition of quantal response equilibrium to this setting, calling it subjective quantal response equilibrium, and study two empirically relevant special cases: (1) Heterogeneus quantal response equilibrium (HQRE), where players share the same, correct beliefs, about the distribution of payoff responsiveness; and (2) Truncated quantal response equilibrium (TQRE), where players systematically underestimate the distribution of the other players' responsiveness. We identify a formal connection between TQRE, and the Cognitive Hierarchy (CH) model, and prove that CH can be approximated arbitrarily closely by TQRE. We conduct a series of experiments designed to di