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

doi:10.1007/s13235-021-00377-0

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^*

^*Corresponding author for this work

Departamento de Matemáticas

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

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 GM_N, 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 GM_N. 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 GM_N.

Original language	English
Pages (from-to)	512-537
Number of pages	26
Journal	Dynamic Games and Applications
Volume	11
Issue number	3
DOIs	https://doi.org/10.1007/s13235-021-00377-0
State	Published - Sep 2021

Bibliographical note

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

Keywords

Discounted criterion
Mean field theory
Systems of interacting objects
Zero-sum games

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10.1007/s13235-021-00377-0

Cite this

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

Abstract

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Keywords

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