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Zero-Sum Ergodic Semi-Markov Games with Weakly Continuous Transition Probabilities

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  • A. Jaśkiewicz

    (Polish Academy of Sciences)

Abstract

Zero-sum ergodic semi-Markov games with weakly continuous transition probabilities and lower semicontinuous, possibly unbounded, payoff functions are studied. Two payoff criteria are considered: the ratio average and the time average. The main result concerns the existence of a lower semicontinuous solution to the optimality equation and its proof is based on a fixed-point argument. Moreover, it is shown that the ratio average as well as the time average payoff stochastic games have the same value. In addition, one player possesses an ε-optimal stationary strategy (ε>0), whereas the other has an optimal stationary strategy.

Suggested Citation

  • A. Jaśkiewicz, 2009. "Zero-Sum Ergodic Semi-Markov Games with Weakly Continuous Transition Probabilities," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 321-347, May.
    • Handle: RePEc:spr:joptap:v:141:y:2009:i:2:d:10.1007_s10957-008-9491-2
    DOI: 10.1007/s10957-008-9491-2
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    References listed on IDEAS

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    1. Nishimura, Kazuo & Stachurski, John, 2007. "Stochastic optimal policies when the discount rate vanishes," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1416-1430, April.
    2. A. Jaśkiewicz, 2004. "On the Equivalence of Two Expected Average Cost Criteria for Semi-Markov Control Processes," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 326-338, May.
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    Cited by:

    1. Yonghui Huang & Zhaotong Lian & Xianping Guo, 2023. "Zero-sum infinite-horizon discounted piecewise deterministic Markov games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(2), pages 179-205, April.
    2. Yonghui Huang & Xianping Guo & Xinyuan Song, 2011. "Performance Analysis for Controlled Semi-Markov Systems with Application to Maintenance," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 395-415, August.

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