[J38] - Learning in nonatomic games, Part I: Finite action spaces and population games

S. Hadikhanloo, R. Laraki, P. Mertikopoulos, and S. Sorin. Journal of Dynamics and Games, W. H. Sandholm memorial issue, forthcoming.

Abstract

We examine the long-run behavior of a wide range of dynamics for learning in nonatomic games, in both discrete and continuous time. The class of dynamics under consideration includes fictitious play and its regularized variants, the best-reply dynamics (again, possibly regularized), as well as the dynamics of dual averaging / “follow the regularized leader” (which in turn includes as special cases the replicator dynamics and Friedman’s projection dynamics). Our analysis concerns both the actual trajectory of play and its time-average, and we cover potential and monotone games, as well as games with an evolutionarily stable state (global or otherwise). We focus exclusively on games with finite action spaces; nonatomic games with continuous action spaces are treated separately in Part II of this paper.

arXiv link: https://arxiv.org/abs/2107.01595

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