  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.
