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Published in:
17-02-2021
A Mean Field Approach for Discounted Zero-Sum Games in a Class of Systems of Interacting Objects
Published in: Dynamic Games and Applications | Issue 3/2021
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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 \(\mathcal {GM}_{N}\).