Testing the Quantal Response Hypothesis

TL;DR

This paper introduces a non-parametric test for the Quantal Response Equilibrium hypothesis, using convex analysis and moment inequalities, and applies it to experimental game data to evaluate its validity.

Contribution

It develops a novel non-parametric testing method for QRE consistency based on cyclic monotonicity, advancing empirical validation techniques in game theory.

Findings

Reject QRE in pooled data

Fail to reject QRE for over half of individual subjects

Demonstrate the test's applicability to experimental data

Abstract

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.