A Policy Improvement Algorithm for Solving a Mixture Class of Perfect Information and AR-AT Semi-Markov Games

P. Mondal, S. K. Neogy (), A. Gupta () and D. Ghorui ()
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P. Mondal: Mathematics Department, Government General Degree College, Ranibandh, Bankura 722135, India
S. K. Neogy: Indian Statistical Institute, Delhi Centre, New Delhi 110016, India
A. Gupta: Indian Statistical Institute, Kolkata Centre, Kolkata 700108, India
D. Ghorui: Mathematics Department, Jadavpur University, Kolkata 700032, India

International Game Theory Review (IGTR), 2020, vol. 22, issue 02, 1-19

Abstract: Zero-sum two-person discounted semi-Markov games with finite state and action spaces are studied where a collection of states having Perfect Information (PI) property is mixed with another collection of states having Additive Reward–Additive Transition and Action Independent Transition Time (AR-AT-AITT) property. For such a PI/AR-AT-AITT mixture class of games, we prove the existence of an optimal pure stationary strategy for each player. We develop a policy improvement algorithm for solving discounted semi-Markov decision processes (one player version of semi-Markov games) and using it we obtain a policy-improvement type algorithm for computing an optimal strategy pair of a PI/AR-AT-AITT mixture semi-Markov game. Finally, we extend our results when the states having PI property are replaced by a subclass of Switching Control (SC) states.

Keywords: Semi-Markov games; perfect information; AR-AT; optimal pure stationary strategies; policy improvement algorithm (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0219198920400083

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