Learning in games using the imprecise Dirichlet model

We propose a new learning model for finite strategic-form two-player games based on fictitious play and Walley’s imprecise Dirichlet model (1996, J. Roy. Statistical Society B 58, 3–57). This model allows the initial beliefs of the players about their opponent’s strategy choice to be near-vacuous or imprecise instead of being precisely defined. A similar generalization can be made as the one proposed by Fudenberg and Kreps (1993, Games Econ. Behav. 5, 320–367) for fictitious play, where assumptions about immediate behavior are replaced with assumptions about asymptotic behavior. We also obtain similar convergence results for this generalization: if there is convergence, it will be to an equilibrium.