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 probabil- ities of the strategy profiles satisfying the concept are unspecified, and all strategies not satisfying it are implicitly assigned probability zero. As an alternative, we re- cast 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 regula- tors can use PGT to make optimal decisions in situations where conventional game theory cannot provide advice.
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