Learning in nonatomic games, Part I: Finite action spaces and population games - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Journal of Dynamics and Games Year : 2022

Learning in nonatomic games, Part I: Finite action spaces and population games

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 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.
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Dates and versions

hal-03342992 , version 1 (13-09-2021)

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Saeed Hadikhanloo, Rida Laraki, Panayotis Mertikopoulos, Sylvain Sorin. Learning in nonatomic games, Part I: Finite action spaces and population games. Journal of Dynamics and Games, 2022, 9 (4), pp.433-460. ⟨10.3934/jdg.2022018⟩. ⟨hal-03342992⟩
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