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Deriving and Analysing Optimal Strategies in Bayesian Models of Games

Author

Listed:
  • S. C. Young

    (ICI Agrochemicals, Jealott's Hill Research Station, Berkshire RG12 6EY, England)

  • J. Q. Smith

    (Department of Statistics, University of Warwick, Coventry CV4 7AL, England)

Abstract

Wilson (1986) gives a backwards induction algorithm for sequentially obtaining the optimal next move in a repeated Bayesian game. In this paper we show how to identify the form of an optimal solution of such a game by a graphical procedure. By means of the Prisoner's Dilemma game, we illustrate how Wilson's algorithm can be enhanced using the derived analytic form of the solution to produce an explicit optimal strategy. We can then determine not only how P 1 should play on all subsequent moves of the game, but also use ideas of Bayes rationality to discuss whether a given model of P 2 's reactions is realistic.

Suggested Citation

  • S. C. Young & J. Q. Smith, 1991. "Deriving and Analysing Optimal Strategies in Bayesian Models of Games," Management Science, INFORMS, vol. 37(5), pages 559-571, May.
    • Handle: RePEc:inm:ormnsc:v:37:y:1991:i:5:p:559-571
    DOI: 10.1287/mnsc.37.5.559
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