Quantal Response Equilibrium with a Continuum of Types: Characterization and Nonparametric Identification

TL;DR

This paper characterizes Quantal Response Equilibrium (QRE) in binary-action games with a continuum of types, providing sharp predictions and nonparametric tests, and applies these methods to experimental data on the compromise game.

Contribution

It offers the first complete nonparametric characterization of QRE in games with a continuum of types and develops tests based on this characterization.

Findings

Sharp predictions for global games, volunteer's dilemma, and compromise game.

Nonparametric tests for QRE are developed and validated.

Empirical analysis revisits experimental data on the compromise game.

Abstract

Quantal response equilibrium (QRE), a statistical generalization of Nash equilibrium, is a standard benchmark in the analysis of experimental data. Despite its influence, nonparametric characterizations and tests of QRE are unavailable beyond the case of finite games. We address this gap by completely characterizing the set of QRE in a class of binary-action games with a continuum of types. Our characterization provides sharp predictions in settings such as global games, volunteer's dilemma, and the compromise game. Further, we leverage our results to develop nonparametric tests of QRE. As an empirical application, we revisit the experimental data from Carrillo and Palfrey (2009) on the compromise game.