Statistical Game Theory

This paper uses the concept of correlated equilibrium to make statistical predictions directly from a standard strategic form game. This paper finds a simple technique for placing bounds on the covariance of people's actions in all correlated equilibria of a game. In a "generic'' $2\times 2$ game, for example, one can predict the sign of the covariance of people's actions. This paper also considers the question of identification: given observations, what games are consistent with these observations. For $2\times 2$ games, for example, a signed covariance in people's actions is sufficient to identify pure strategy Nash equilibria of the game. An application to spatial data analysis is also discussed.