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Completely mixed strategies for single controller unichain semi-Markov games with undiscounted payoffs

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  • Prasenjit Mondal

    (Government of West Bengal)

Abstract

Zero-sum two-person finite undiscounted (limiting ratio average) semi-Markov games are considered where the transition probabilities and the transition times are controlled by a fixed player in all states. We prove that if such a game is unichain, the value and optimal stationary strategies can be obtained from an optimal solution of a linear programming algorithm for the associated undiscounted unichain single controller stochastic game (obtained by a data transformation method). The single controller undiscounted unichain semi-Markov games have been formulated as a linear complementarity problem and solved using a stepwise principal pivoting algorithm. We provide necessary and sufficient conditions for such games to be completely mixed (i.e., every optimal stationary strategy for each player assigns a positive probability to every action in every state). Some properties analogous to completely mixed matrix games are also established in this paper.

Suggested Citation

  • Prasenjit Mondal, 2018. "Completely mixed strategies for single controller unichain semi-Markov games with undiscounted payoffs," Operational Research, Springer, vol. 18(2), pages 451-468, July.
    • Handle: RePEc:spr:operea:v:18:y:2018:i:2:d:10.1007_s12351-016-0272-7
    DOI: 10.1007/s12351-016-0272-7
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    References listed on IDEAS

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