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

Prasenjit Mondal ()
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Prasenjit Mondal: Government of West Bengal

Operational Research, 2018, vol. 18, issue 2, No 8, 468 pages

Abstract: 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.

Keywords: Semi-Markov games; Undiscounted payoffs; Single controller semi-Markov games; Completely mixed strategies; Linear complementarity problem; Principal pivot transform; 91A15; 90C33 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s12351-016-0272-7

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