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Existence of nash equilibria for constrained stochastic games

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  • Jorge Alvarez-Mena
  • Onésimo Hernández-Lerma

Abstract

In this paper, we consider constrained noncooperative N-person stochastic games with discounted cost criteria. The state space is assumed to be countable and the action sets are compact metric spaces. We present three main results. The first concerns the sensitivity or approximation of constrained games. The second shows the existence of Nash equilibria for constrained games with a finite state space (and compact actions space), and, finally, in the third one we extend that existence result to a class of constrained games which can be “approximated” by constrained games with finitely many states and compact action spaces. Our results are illustrated with two examples on queueing systems, which clearly show some important differences between constrained and unconstrained games. Copyright Springer-Verlag 2006

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:63:y:2006:i:2:p:261-285
    DOI: 10.1007/s00186-005-0003-y
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    References listed on IDEAS

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    Cited by:

    1. Wenzhao Zhang, 2019. "Discrete-Time Constrained Average Stochastic Games with Independent State Processes," Mathematics, MDPI, vol. 7(11), pages 1-18, November.
    2. Guo, Xianping & Zhang, Wenzhao, 2014. "Convergence of controlled models and finite-state approximation for discounted continuous-time Markov decision processes with constraints," European Journal of Operational Research, Elsevier, vol. 238(2), pages 486-496.

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