Testing the Foundations of Quantal Response Equilibrium

Abstract

Quantal response equilibrium (QRE) has become a popular alternative to the standard Nash equilibrium concept in game theoretic applications. It is well known that human subjects do not regularly choose Nash equilibrium strategies. It has been hypothesized that subjects are limited by strategic uncertainty or that subjects have broader social preferences over the outcome of games. These two factors, among others, make subjects boundedly-rational. QRE, in essence, adds a logistic error function to the strict, knife-edge predictions of Nash equilibria. What makes QRE appealing, however, also makes it very difficult to test, because almost any observed behavior may be consistent with different parameterizations of the error function. We present the first steps of a research program designed to strip away the underlying causes of the strategic errors thought to be modeled by QRE. If these causes of strategic error are correct explanations for the deviations, then their removal should enable subjects to choose Nash equilibrium strategies. We find, however, that subjects continue to deviate from predictions even when the reasons presumed by QRE are removed. Moreover, the deviations are different for each and every game, and thus QRE would require the same subjects to have different error parameterizations. While we need more expansive testing of the various causes of strategic error, in our judgment, therefore, QRE is not useful at predicting human behavior, and is of limited use in explaining human behavior across even a small range of similar decisions.