A Mean Field Approach for Discounted Zero-Sum Games in a Class of Systems of Interacting Objects

Carmen G. Higuera-Chan, J. Adolfo Minjárez-Sosa*

*Autor correspondiente de este trabajo

Resultado de la investigación: Contribución a una revistaArtículorevisión exhaustiva

2 Citas (Scopus)

Resumen

The paper deals with systems composed of a large number of N interacting objects (e.g., agents, particles) controlled by two players defining a stochastic zero-sum game. The objects can be classified according to a finite set of classes or categories over which they move randomly. Because N is too large, the game problem is studied following a mean field approach. That is, a zero-sum game model GMN, where the states are the proportions of objects in each class, is introduced. Then, letting N→ ∞ (the mean field limit) we obtain a new game model GM, independent on N, which is easier to analyze than GMN. Considering a discounted optimality criterion, our objective is to prove that an optimal pair of strategies in GM is an approximate optimal pair as N→ ∞ in the original game model GMN.

Idioma originalInglés
Páginas (desde-hasta)512-537
Número de páginas26
PublicaciónDynamic Games and Applications
Volumen11
N.º3
DOI
EstadoPublicada - sep 2021

Nota bibliográfica

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature.

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