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Nonzero-sum games for continuous-time Markov chains with unbounded discounted payoffs

Part of: Game theory

Published online by Cambridge University Press:  14 July 2016

Xianping Guo  and
Onésimo Hernández-Lerma
Xianping Guo*
Affiliation:
CINVESTAV and Zhongshan University
Onésimo Hernández-Lerma*
Affiliation:
CINVESTAV
*
∗Postal address: Department of Mathematics, Zhongshan University, Guangzhou, 510275, PR China. Email address: [email protected]
∗∗Postal address: Department of Mathematics, CINVESTAV IPN, A. Postal 14-740, Mexico DF 07000, Mexico. Email address: [email protected]
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Abstract

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In this paper, we study two-person nonzero-sum games for continuous-time Markov chains with discounted payoff criteria and Borel action spaces. The transition rates are possibly unbounded, and the payoff functions might have neither upper nor lower bounds. We give conditions that ensure the existence of Nash equilibria in stationary strategies. For the zero-sum case, we prove the existence of the value of the game, and also provide a recursive way to compute it, or at least to approximate it. Our results are applied to a controlled queueing system. We also show that if the transition rates are uniformly bounded, then a continuous-time game is equivalent, in a suitable sense, to a discrete-time Markov game.

Keywords

Nonzero-sum gamediscounted payoff criterionNash equilibriumcontrolled Q-process

MSC classification

Primary: 91A15: Stochastic games 91A25: Dynamic games
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 2 , June 2005 , pp. 303 - 320
Copyright
© Applied Probability Trust 2005 

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