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

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 important in this framework. If the payoffs that explain 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 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 can be explained by payoff matrices for which Nash equilibria are efficiently computable.