Deriving and Analysing Optimal Strategies in Bayesian Models of Games

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 P₁ should play on all subsequent moves of the game, but also use ideas of Bayes rationality to discuss whether a given model of P₂'s reactions is realistic.