Statistical prediction of the outcome of a noncooperative game

Many statistics problems involve predicting the joint strategy of players in a noncooperative game. Conventional game theory predicts the joint strategy will satisfy an "equilibrium concept". Relative probabilities of the joint strategies satisfying the equilibrium concept are unspecified, and all joint strategies not satisfying it are assigned probability zero.

As an alternative, I cast the prediction problem as one of statistical inference. In this alternative the "data" is the game specification, which induces a posterior probability distribution over all joint strategies. I show that this alternative provides a unique best prediction for any noncooperative game, thereby solving a long-standing problem of conventional game theory. I also present an application of this alternative to predicting the behavior of a set of airlines during a weather disruption. In particular I show how to sample from the posterior distribution of airline joint strategies, and how to estimate associated quantities like covariances in airline behavior.