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

Author

Listed:
  • 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)

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.

Suggested Citation

  • P. Mondal & S. K. Neogy & A. Gupta & D. Ghorui, 2020. "A Policy Improvement Algorithm for Solving a Mixture Class of Perfect Information and AR-AT Semi-Markov Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 22(02), pages 1-19, June.
    • Handle: RePEc:wsi:igtrxx:v:22:y:2020:i:02:n:s0219198920400083
    DOI: 10.1142/S0219198920400083
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    Cited by:

    1. Sina Nayeri & Mahdieh Tavakoli & Mehrab Tanhaeean & Fariborz Jolai, 2022. "A robust fuzzy stochastic model for the responsive-resilient inventory-location problem: comparison of metaheuristic algorithms," Annals of Operations Research, Springer, vol. 315(2), pages 1895-1935, August.

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