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

Carmen G. Higuera-Chan () and J. Adolfo Minjárez-Sosa ()
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Carmen G. Higuera-Chan: Universidad de Sonora
J. Adolfo Minjárez-Sosa: Universidad de Sonora

Dynamic Games and Applications, 2021, vol. 11, issue 3, No 4, 512-537

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

Keywords: Zero-sum games; Systems of interacting objects; Mean field theory; Discounted criterion; 91A15; 91A50; 60K35 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s13235-021-00377-0

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