TY - JOUR

T1 - A Mean Field Approach for Discounted Zero-Sum Games in a Class of Systems of Interacting Objects

AU - Higuera-Chan, Carmen G.

AU - Minjárez-Sosa, J. Adolfo

N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature.

PY - 2021/9

Y1 - 2021/9

N2 - 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.

AB - 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.

KW - Discounted criterion

KW - Mean field theory

KW - Systems of interacting objects

KW - Zero-sum games

UR - http://www.scopus.com/inward/record.url?scp=85101154342&partnerID=8YFLogxK

U2 - 10.1007/s13235-021-00377-0

DO - 10.1007/s13235-021-00377-0

M3 - Artículo

AN - SCOPUS:85101154342

VL - 11

SP - 512

EP - 537

JO - Dynamic Games and Applications

JF - Dynamic Games and Applications

SN - 2153-0785

IS - 3

ER -