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

Research output: Contribution to journalArticlepeer-review

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 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.

Original languageEnglish
Pages (from-to)512-537
Number of pages26
JournalDynamic Games and Applications
Volume11
Issue number3
DOIs
StatePublished - Sep 2021

Bibliographical note

Funding Information:
Work was partially supported by Consejo Nacional de Ciencia y Tecnolog?a (CONACYT-M?xico) under grant Ciencia Frontera 2019-87787.

Funding Information:
Work was partially supported by Consejo Nacional de Ciencia y Tecnología (CONACYT-México) under grant Ciencia Frontera 2019-87787.

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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