Testing the Quantal Response Hypothesis

This paper develops a formal test for consistency of players' behavior in a series of games with the quantal response equilibrium (QRE). The test exploits a characterization of the equilibrium choice probabilities in a QRE as the gradient of a convex function, which thus satisfies the cyclic monotonicity inequalities. Our testing procedure utilizes recent econometric results for moment inequality models. We assess the performance of the test using both Monte Carlo simulation and lab experimental data from a series of generalized matching pennies games. Our experimental findings are consistent with the literature: the joint hypothesis of QRE, risk neutrality and player role homogeneity is rejected in the pooled data, but cannot be rejected in the individual data for over half of the subjects. By considering subsets of cycle monotonicity inequalities, our approach also highlights the nature of QRE consistency violations.