Testing the Quantal Response Hypothesis

Abstract

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.

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