Statistical Prediction of the Outcome of a Noncooperative Game

66 Pages Posted: 28 Jul 2008 Last revised: 1 Sep 2009

See all articles by David Wolpert

David Wolpert

Santa Fe Institute

James Bono

Microsoft Corporation

Date Written: September 25, 2008


Conventionally, game theory predicts that the joint mixed strategy of players in a noncooperative game will satisfy some equilibrium concept. Relative probabilities of the joint strategies satisfying the concept are unspecified, and all strategies not satisfying it are assigned probability zero. As an alternative, we recast the prediction problem of game theory as statistically estimating the joint strategy, 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 joint strategies 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.

Keywords: Multi-agent systems, Noncooperative Games, Quantal Response Equilibrium, Bayesian Statistics, Statistical Physics

JEL Classification: C02, C11, C70, C72

Suggested Citation

Wolpert, David and Bono, James, Statistical Prediction of the Outcome of a Noncooperative Game (September 25, 2008). Available at SSRN: or

David Wolpert (Contact Author)

Santa Fe Institute ( email )

1399 Hyde Park Road
Santa Fe, NM 897501
United States

James Bono

Microsoft Corporation ( email )

One Microsoft Way
Redmond, WA 98052
United States

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