Testing the Quantal Response Hypothesis
  This paper develops a non-parametric 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 any structural 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 our test using lab experimental data from a series of generalized matching pennies games. We reject the QRE hypothesis in the pooled data, but it cannot be rejected in the individual data for over half of the subjects. 
Kirill Pogorelskiy, Emerson Melo, Matthew Shum
stat.AP cs.GT