Zero-sum games for continuous-time Markov chains with unbounded transition and average payoff rates
Authors:
- Xianping GuoXGXianping Guo
- Onésimo Hernández-LermaOHOnésimo Hernández-Lerma
- 1 June 2003
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 40 (2) , 327-345
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
This publication has 25 references indexed in Scilit:
- Drift and monotonicity conditions for continuous-time controlled markov chains with an average criterionIEEE Transactions on Automatic Control, 2003
- Continuous-time controlled Markov chainsThe Annals of Applied Probability, 2003
- A note on optimality conditions for continuous-time Markov decision processes with average cost criterionIEEE Transactions on Automatic Control, 2001
- A convergence method for stochastic differential games with a small parameterStochastic Analysis and Applications, 1999
- Stochastic Games with Average Payoff CriterionApplied Mathematics & Optimization, 1998
- Contraction Conditions for Average and α-Discount Optimality in Countable State Markov Games with Unbounded RewardsMathematics of Operations Research, 1997
- Denumerable state stochastic games with limiting average payoffJournal of Optimization Theory and Applications, 1993
- Stochastic differential games: Occupation measure based approachJournal of Optimization Theory and Applications, 1992
- Continuous time control of Markov processes on an arbitrary state space: Average return criterionStochastic Processes and their Applications, 1976
- On the integro-differential equations of purely discontinuous Markoff processesTransactions of the American Mathematical Society, 1940