Learning in nonatomic games, Part I: Finite action spaces and population games
This work addresses theoretical foundations for learning in large-scale games, relevant for economics and multi-agent systems, but is incremental as it extends existing dynamics to nonatomic settings.
The paper analyzes the long-run behavior of various learning dynamics in nonatomic games with finite action spaces, covering dynamics like fictitious play and best-reply, and applies this to potential, monotone, and evolutionarily stable games.
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 themselves include 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 in detail in Part II of this paper.