Statistical prediction of the outcome of a noncooperative game
Conventionally, game theory predicts that the mixed strategy proﬁle of players in a noncooperative game will satisfy some equilibrium concept. Relative probabilities of the strategy proﬁles satisfying the concept are unspeciﬁed, and all strategies not satisfying it are implicitly assigned probability zero. As an alternative, we recast the prediction problem of game theory as statistically estimating the strategy proﬁle, from “data” that consists of the game speciﬁcation. This replaces the focus of game theory, on specifying a set of “equilibrium” mixed strategies, with a new focus, on specifying a probability density over all mixed strategies. We explore a Bayesian version of such a Predictive Game Theory (PGT). We show that for some games the peaks of the posterior over strategy proﬁles approximate quantal response equilibria. We also show how PGT provides a best single prediction for any noncooperative game, i.e., a universal reﬁnement. We also show how regulators can use PGT to make optimal decisions in situations where conventional game theory cannot provide advice.