S. Hadikhanloo, R. Laraki, P. Mertikopoulos, and S. Sorin. Working paper.
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