Statistical prediction of the outcome of a noncooperative game
AbstractConventionally, 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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Bibliographic InfoPaper provided by American University, Department of Economics in its series Working Papers with number 2009-20.
Date of creation: Oct 2009
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Quantal Response Equilibrium; Bayesian Statistics; Entropic prior; Maximum entropy;
Find related papers by JEL classification:
- C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
- C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
- C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-12-05 (All new papers)
- NEP-EVO-2009-12-05 (Evolutionary Economics)
- NEP-GTH-2009-12-05 (Game Theory)
- NEP-HPE-2009-12-05 (History & Philosophy of Economics)
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