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 [P. Walley, Inferences from multinomial data: learning about a bag of marbles, J. Roy. Statist. Soc. B 58 (1996) 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 [D. Fudenberg, D.M. Kreps, Learning mixed equilibria, Games Econ. Behav. 5 (1993) 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.