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.
Bibliographical noteFunding Information:
Work was partially supported by Consejo Nacional de Ciencia y Tecnología (CONACYT-México) under grant Ciencia Frontera 2019-87787.
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature.
- Discounted criterion
- Mean field theory
- Systems of interacting objects
- Zero-sum games