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Perfect information two-person zero-sum markov games with imprecise transition probabilities

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  • Hyeong Chang

Abstract

Based on an extension of the controlled Markov set-chain model by Kurano et al. (in J Appl Prob 35:293–302, 1998) into competitive two-player game setting, we provide a model of perfect information two-person zero-sum Markov games with imprecise transition probabilities. We define an equilibrium value for the games formulated with the model in terms of a partial order and then establish the existence of an equilibrium policy pair that achieves the equilibrium value. We further analyze finite-approximation error bounds obtained from a value iteration-type algorithm and discuss some applications of the model. Copyright Springer-Verlag 2006

Suggested Citation

  • Hyeong Chang, 2006. "Perfect information two-person zero-sum markov games with imprecise transition probabilities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(2), pages 335-351, October.
    • Handle: RePEc:spr:mathme:v:64:y:2006:i:2:p:335-351
    DOI: 10.1007/s00186-006-0081-5
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    References listed on IDEAS

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    1. Chelsea C. White & Hany K. Eldeib, 1994. "Markov Decision Processes with Imprecise Transition Probabilities," Operations Research, INFORMS, vol. 42(4), pages 739-749, August.
    2. Jay K. Satia & Roy E. Lave, 1973. "Markovian Decision Processes with Uncertain Transition Probabilities," Operations Research, INFORMS, vol. 21(3), pages 728-740, June.
    3. J. K. Satia & R. E. Lave, 1973. "Markovian Decision Processes with Probabilistic Observation of States," Management Science, INFORMS, vol. 20(1), pages 1-13, September.
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