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Statistical prediction of the outcome of a noncooperative game

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Listed:
  • James W. Bono
  • David H. Wolpert

Abstract

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.

Suggested Citation

  • James W. Bono & David H. Wolpert, 2009. "Statistical prediction of the outcome of a noncooperative game," Working Papers 2009-20, American University, Department of Economics.
  • Handle: RePEc:amu:wpaper:2009-20
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Ellis Scharfenaker, 2015. "A Quantal Response Model of Firm Competition," Working Papers 1507, New School for Social Research, Department of Economics.
    2. James Costain & Anton Nakov, 2013. "Logit price dynamics," Working Papers 1301, Banco de España;Working Papers Homepage.
    3. James Costain, 2017. "Costly decisions and sequential bargaining," Working Papers 1729, Banco de España;Working Papers Homepage.

    More about this item

    Keywords

    Quantal Response Equilibrium; Bayesian Statistics; Entropic prior; Maximum entropy;

    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

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