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Zero-Sum Markov Games with Random State-Actions-Dependent Discount Factors: Existence of Optimal Strategies

Author

Listed:
  • David González-Sánchez

    (CONACYT–Universidad de Sonora)

  • Fernando Luque-Vásquez

    (Universidad de Sonora)

  • J. Adolfo Minjárez-Sosa

    (Universidad de Sonora)

Abstract

This work deals with a class of discrete-time zero-sum Markov games under a discounted optimality criterion with random state-actions-dependent discount factors of the form $$\tilde{\alpha }(x_{n},a_{n},b_{n},\xi _{n+1})$$ α ~ ( x n , a n , b n , ξ n + 1 ) , where $$x_{n}, a_{n}, b_{n}$$ x n , a n , b n , and $$\xi _{n+1}$$ ξ n + 1 are the state, the actions of players, and a random disturbance at time n, respectively, taking values in Borel spaces. Assuming possibly unbounded payoff, we prove the existence of a value of the game as well as a stationary pair of optimal strategies.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:dyngam:v:9:y:2019:i:1:d:10.1007_s13235-018-0248-8
    DOI: 10.1007/s13235-018-0248-8
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    References listed on IDEAS

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    Cited by:

    1. John Stachurski & Junnan Zhang, 2019. "Dynamic Programming with State-Dependent Discounting," Papers 1908.08800, arXiv.org, revised Oct 2020.
    2. 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.

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