Learning in nonatomic games, Part I: Finite action spaces and population games
Hadikhanloo, Saeed; Laraki, Rida; Mertikopoulos, Panayotis; Sorin, Sylvain (2021), Learning in nonatomic games, Part I: Finite action spaces and population games. https://basepub.dauphine.psl.eu/handle/123456789/22294
TypeDocument de travail / Working paper
Series titlePreprint Lamsade
MetadataShow full item record
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Performance analysis and optimization of LARge Infrastructures and Systems [POLARIS ]
Institut de Mathématiques de Jussieu - Paris Rive Gauche [IMJ-PRG (UMR_7586)]
Abstract (EN)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.
Subjects / KeywordsLearning Theory; Nonatomic games; Fictitious play; Dual averaging; Evolutionary stability; Nash equilibrium; Variational inequalities
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