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Zero-sum games for continuous-time Markov chains with unbounded transition and average payoff rates

Part of: Game theory Markov processes

Published online by Cambridge University Press:  14 July 2016

Xianping Guo  and
Onésimo Hernández-Lerma
Xianping Guo*
Affiliation:
Zhongshan University
Onésimo Hernández-Lerma*
Affiliation:
Centro de Investigación y de Estudios, Avanzados del IPN, Mexico
*
∗ Postal address: The School of Mathematics and Computational Science, Zhongshan University, Guangzhou 510275, People's Republic of China.
∗∗ Postal address: Departamento de Matemáticas, CINVESTAV-IPN, Apartado Postal 14-740, México D.F. 07000, Mexico. Email address: ohernand@math.cinvestav.mx
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Abstract

This paper is a first study of two-person zero-sum games for denumerable continuous-time Markov chains determined by given transition rates, with an average payoff criterion. The transition rates are allowed to be unbounded, and the payoff rates may have neither upper nor lower bounds. In the spirit of the ‘drift and monotonicity’ conditions for continuous-time Markov processes, we give conditions on the controlled system's primitive data under which the existence of the value of the game and a pair of strong optimal stationary strategies is ensured by using the Shapley equations. Also, we present a ‘martingale characterization’ of a pair of strong optimal stationary strategies. Our results are illustrated with a birth-and-death game.

Keywords

Zero-sum gamecontrolled Q—processaverage payoff criterionpairs of optimal stationary strategiesmartingale characterization

MSC classification

Primary: 91A15: Stochastic games 91A25: Dynamic games 60J27: Continuous-time Markov processes on discrete state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 2 , June 2003 , pp. 327 - 345
Copyright
Copyright © Applied Probability Trust 2003 

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