Testing the Quantal Response Hypothesis

We develop a non-parametric test for consistency of player behavior with the Quantal Response Equilibrium (QRE). The test exploits a characterization of the equilibrium choice probabilities in any structural QRE as the gradient of a convex function; thereby QRE-consistent choices satisfy the cyclic monotonicity inequalities. Our testing procedure utilizes recent econometric results for moment inequality models. We assess our test using lab experimental data from a series of generalized matching pennies games. We reject the QRE hypothesis in the pooled data but cannot reject individual-level quantal response behavior for over half of the subjects