Quantal Response Equilibrium with Symmetry: Representation and Applications
We study an axiomatic variant of quantal response equilibrium (QRE) for normal form games that augments the regularity axioms (Goeree et al., 2005) with various forms of “symmetry” across players and actions. The model refines regular QRE, generalizes logit QRE, and is tractable in many applications. The main result is a representation theorem that characterizes the model’s set-valued predictions by taking unions and intersections of simple sets. We completely characterize the predictions for (almost) all 2x2 games, a corollary of which is to show, in coordination games, which Nash equilibrium is selected by the principal branch of the logit correspondence. As applications, we consider three classic games: public goods provision with heterogenous costs of participation, jury voting with unanimity, and the infinitely repeated prisoner’s dilemma. For each, we characterize all equilibria within a particular large class. An analysis of existing experiments shows the model’s potential for organizing experimental data.