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

Author

Listed:
  • Carmen G. Higuera-Chan

    (Universidad de Sonora)

  • J. Adolfo Minjárez-Sosa

    (Universidad de Sonora)

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 .

Suggested Citation

  • Carmen G. Higuera-Chan & J. Adolfo Minjárez-Sosa, 2021. "A Mean Field Approach for Discounted Zero-Sum Games in a Class of Systems of Interacting Objects," Dynamic Games and Applications, Springer, vol. 11(3), pages 512-537, September.
  • Handle: RePEc:spr:dyngam:v:11:y:2021:i:3:d:10.1007_s13235-021-00377-0
    DOI: 10.1007/s13235-021-00377-0
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    References listed on IDEAS

    as
    1. Adriana Piazza & Bernardo Pagnoncelli, 2015. "The stochastic Mitra–Wan forestry model: risk neutral and risk averse cases," Journal of Economics, Springer, vol. 115(2), pages 175-194, June.
    2. David González-Sánchez & Fernando Luque-Vásquez & J. Adolfo Minjárez-Sosa, 2019. "Zero-Sum Markov Games with Random State-Actions-Dependent Discount Factors: Existence of Optimal Strategies," Dynamic Games and Applications, Springer, vol. 9(1), pages 103-121, March.
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    Cited by:

    1. Hanshan Li & Yun Hao & Xiaoqian Zhang, 2022. "Offensive/Defensive Game Target Damage Assessment Mathematical Calculation Method between the Projectile and Target," Mathematics, MDPI, vol. 10(22), pages 1-15, November.

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