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The paper studies the highly prototypical Fictitious Play (FP) algorithm, aswell as a broad class of learning processes based on best-response dynamics,that we refer to as FP-type algorithms. A well-known shortcoming of FP is that,while players may learn an equilibrium strategy in some abstract sense, thereare no guarantees that the period-by-period strategies generated by thealgorithm actually converge to equilibrium themselves. This issue isfundamentally related to the discontinuous nature of the best responsecorrespondence and is inherited by many FP-type algorithms. Not only does itcause problems in the interpretation of such algorithms as a mechanism foreconomic and social learning, but it also greatly diminishes the practicalvalue of these algorithms for use in distributed control. We refer to forms oflearning in which players learn equilibria in some abstract sense only (to bedefined more precisely in the paper) as weak learning, and we refer to forms oflearning where players' period-by-period strategies converge to equilibrium asstrong learning. An approach is presented for modifying an FP-type algorithmthat achieves weak learning in order to construct a variant that achievesstrong learning. Theoretical convergence results are proved.

From Weak Learning to Strong Learning in Fictitious Play Type Algorithms