Zero-Sum Markov Games with Random State-Actions-Dependent Discount Factors

Existence of Optimal Strategies

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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 α~ (x n , a n , b n , ξ n + 1 ) , where x n , a n , b n , and 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.

Original languageEnglish
Pages (from-to)103-121
Number of pages19
JournalDynamic Games and Applications
Volume9
Issue number1
DOIs
StatePublished - 15 Mar 2019

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Discount Factor
Zero-sum
Optimal Strategy
Game
Dependent
Optimality Criteria
Discrete-time
Disturbance
Class
Form

Keywords

  • Discounted optimality
  • Markov games
  • Nonconstant discount factor

Cite this

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title = "Zero-Sum Markov Games with Random State-Actions-Dependent Discount Factors: Existence of Optimal Strategies",
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AU - González-Sánchez, David

AU - Luque-Vásquez, Fernando

AU - Minjárez-Sosa, J. Adolfo

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N2 - 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 α~ (x n , a n , b n , ξ n + 1 ) , where x n , a n , b n , and 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.

AB - 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 α~ (x n , a n , b n , ξ n + 1 ) , where x n , a n , b n , and 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.

KW - Discounted optimality

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KW - Nonconstant discount factor

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