Existence of nash equilibria for constrained stochastic games |
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Authors: | Jorge Alvarez-Mena Onésimo Hernández-Lerma |
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Affiliation: | (1) Programa de Investigación en Matemáticas Aplicadas y Computación, IMP, A Postal 14-805, México, D.F. 07730, México;(2) Present address: Departamento de Ciencias Básicas, UAT, A. Postal 140, Apizaco, Tlaxcala, 90300, México;(3) Departamento de Matemáticas, CINVESTAV-IPN, A. Postal 14-740, México, D.F. 07000, México |
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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.Mathematics Subject Classification (2000): Primary: 91A15. 91A10; Secondary: 90C40 |
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Keywords: | Constrained Markov games Nash equilibria Constrained Markov control processes |
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