On the Existence of Low-Rank Explanations for Mixed Strategy Behavior

Abstract

Nash equilibrium is used as a model to explain the observed behavior of players in strategic settings. For example, in many empirical applications we observe player behavior, and the problem is to determine if there exist payoffs for the players for which the equilibrium corresponds to observed player behavior. Computational complexity of Nash equilibria is an important consideration in this framework. If the instance of the model that explains observed player behavior requires players to have solved a computationally hard problem, then the explanation provided is questionable. In this paper we provide conditions under which Nash equilibrium is a reasonable explanation for strategic behavior, i.e., conditions under which observed behavior of players can be explained by games in which Nash equilibria are easy to compute. We identify three structural conditions and show that if the data set of observed behavior satisfies any of these conditions, then it is consistent with payoff matrices for which the observed Nash equilibria could have been computed efficiently. Our conditions admit large and structurally complex data sets of observed behavior, showing that even with complexity considerations, Nash equilibrium is often a reasonable model.