**Tuesday 25**^{th} March

10.30am Eagle House, Meeting Room

Professor David H. Wolpert, Santa Fe Institute

http://davidwolpert.weebly.com

**Statistical Prediction of the outcome of an noncooperative game**

Conventionally, game theory predicts that the strategy profile of the players in a noncooperative game will satisfy some equilibrium concept. Relative probabilities of the profiles satisfying the concept are unspecified, and all profile not satisfying it are assigned probability zero.

As an alternative, I recast the positive problem of game theory as statistically estimating the strategy profile from ``data'' of the game specification. This replaces the focus on a set of equilibrium profiles with a focus on a probability density over profiles. I explore a Bayesian version of such a Predictive Game Theory (PGT). I show that for some games the peaks of the posterior over profiles approximate quantal response equilibria - but in other games does not.

I also show how PGT specifies a best single prediction for any noncooperative game, i.e., a universal refinement. It also provides statistical information (e.g., posterior variances) concerning that

prediction that are not provided by conventional game theory. Another major benefit is that PGT recasts and extends "mechanism design", as an exercise in Bayesian decision theory *for the external regulator

designing the mechanism*.

I end with two demonstations of PGT. The first is to predict behaviour of a set of airlines during a weather disruption. In particular I show how to sample from the posterior distribution of airline strategy

profiles, and how to estimate associated quantities like covariances in airline behavior. The second example is a Cournot duopoly, where I show how to use PGT to optimally set tax rates.