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dec 2005 Zero-sum continuous-time Markov games with unbounded transition and discounted payoff rates
Xianping Guo, Onésimo Hernández-Lerma
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Bernoulli 11(6): 1009-1029 (dec 2005). DOI: 10.3150/bj/1137421638

Abstract

This paper is concerned with two-person zero-sum games for continuous-time Markov chains, with possibly unbounded payoff and transition rate functions, under the discounted payoff criterion. We give conditions under which the existence of the value of the game and a pair of optimal stationary strategies is ensured by using the optimality (or Shapley) equation. We prove the convergence of the value iteration scheme to the game's value and to a pair of optimal stationary strategies. Moreover, when the transition rates are bounded we further show that the convergence of value iteration is exponential. Our results are illustrated with a controlled queueing system with unbounded transition and reward rates.

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Xianping Guo. Onésimo Hernández-Lerma. "Zero-sum continuous-time Markov games with unbounded transition and discounted payoff rates." Bernoulli 11 (6) 1009 - 1029, dec 2005. https://doi.org/10.3150/bj/1137421638

Information

Published: dec 2005
First available in Project Euclid: 16 January 2006

zbMATH: 1125.91016
MathSciNet: MR2188839
Digital Object Identifier: 10.3150/bj/1137421638

Rights: Copyright © 2005 Bernoulli Society for Mathematical Statistics and Probability

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Vol.11 • No. 6 • dec 2005
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