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Discrete-Time Constrained Average Stochastic Games with Independent State Processes

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  • Wenzhao Zhang

    (College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, China)

Abstract

In this paper, we consider the discrete-time constrained average stochastic games with independent state processes. The state space of each player is denumerable and one-stage cost functions can be unbounded. In these game models, each player chooses an action each time which influences the transition probability of a Markov chain controlled only by this player. Moreover, each player needs to pay some costs which depend on the actions of all the players. First, we give an existence condition of stationary constrained Nash equilibria based on the technique of average occupation measures and the best response linear program. Then, combining the best response linear program and duality program, we present a non-convex mathematic program and prove that each stationary Nash equilibrium is a global minimizer of this mathematic program. Finally, a controlled wireless network is presented to illustrate our main results.

Suggested Citation

  • Wenzhao Zhang, 2019. "Discrete-Time Constrained Average Stochastic Games with Independent State Processes," Mathematics, MDPI, vol. 7(11), pages 1-18, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1089-:d:285753
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    References listed on IDEAS

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    1. Jorge Alvarez-Mena & Onésimo Hernández-Lerma, 2002. "Convergence of the optimal values of constrained Markov control processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(3), pages 461-484, June.
    2. Wenzhao Zhang & Yonghui Huang & Xianping Guo, 2014. "Nonzero-sum constrained discrete-time Markov games: the case of unbounded costs," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 1074-1102, October.
    3. Jorge Alvarez-Mena & Onésimo Hernández-Lerma, 2002. "Convergence of the optimal values of constrained Markov control processes," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 55(3), pages 461-484, June.
    4. Jorge Alvarez-Mena & Onésimo Hernández-Lerma, 2006. "Existence of nash equilibria for constrained stochastic games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(2), pages 261-285, May.
    5. Andrzej Nowak, 2006. "Remarks on sensitive equilibria in stochastic games with additive reward and transition structure," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(3), pages 481-494, December.
    6. Andrzej Nowak, 2007. "On stochastic games in economics," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(3), pages 513-530, December.
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