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17-02-2021

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

Authors: Carmen G. Higuera-Chan, J. Adolfo Minjárez-Sosa

Published in: Dynamic Games and Applications | Issue 3/2021

## 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 $$\mathcal {GM}_{N}$$, where the states are the proportions of objects in each class, is introduced. Then, letting $$N\rightarrow \infty$$ (the mean field limit) we obtain a new game model $$\mathcal {GM}$$, independent on N, which is easier to analyze than $$\mathcal {GM}_{N}$$. Considering a discounted optimality criterion, our objective is to prove that an optimal pair of strategies in $$\mathcal {GM}$$ is an approximate optimal pair as $$N\rightarrow \infty$$ in the original game model $$\mathcal {GM}_{N}$$.

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Appendix
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Title
A Mean Field Approach for Discounted Zero-Sum Games in a Class of Systems of Interacting Objects
Authors
Carmen G. Higuera-Chan
Publication date
17-02-2021
Publisher
Springer US
Published in
Dynamic Games and Applications / Issue 3/2021
Print ISSN: 2153-0785
Electronic ISSN: 2153-0793
DOI
https://doi.org/10.1007/s13235-021-00377-0

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