Linear Programming and Zero-Sum Two-Person Undiscounted Semi-Markov Games

Prasenjit Mondal ()
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Prasenjit Mondal: Mathematics Department, Chandernagore College (Government), Chandernagore 712136, Hooghly, India

Asia-Pacific Journal of Operational Research (APJOR), 2015, vol. 32, issue 06, 1-20

Abstract: In this paper, zero-sum two-person finite undiscounted (limiting average) semi-Markov games (SMGs) are considered. We prove that the solutions of the game when both players are restricted to semi-Markov strategies are solutions for the original game. In addition, we show that if one player fixes a stationary strategy, then the other player can restrict himself in solving an undiscounted semi-Markov decision process associated with that stationary strategy. The undiscounted SMGs are also studied when the transition probabilities and the transition times are controlled by a fixed player in all states. If such games are unichain, we prove that the value and optimal stationary strategies of the players can be obtained from an optimal solution of a linear programming algorithm. We propose a realistic and generalized traveling inspection model that suitably fits into the class of one player control undiscounted unichain semi-Markov games.

Keywords: Semi-Markov games; limiting average payoffs; one player control semi-Markov games; LP algorithms; traveling inspection problems (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (3)

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DOI: 10.1142/S0217595915500438

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