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Ordered Field Property In A Subclass Of Finite Ser-Sit Semi-Markov Games

Author

Listed:
  • PRASENJIT MONDAL

    (Mathematics Department, Jadavpur University, Kolkata-700032, India)

  • SAGNIK SINHA

    (Mathematics Department, Jadavpur University, Kolkata-700032, India)

Abstract

In this paper, we deal with a subclass of two-person finite SeR-SIT (Separable Reward-State Independent Transition) semi-Markov games which can be solved by solving a single matrix/bimatrix game under discounted as well as limiting average (undiscounted) payoff criteria. A SeR-SIT semi-Markov game does not satisfy the so-called (Archimedean) ordered field property in general. Besides, the ordered field property does not hold even for a SeR-SIT-PT (Separable Reward-State-Independent Transition Probability and Time) semi-Markov game, which is a natural version of a SeR-SIT stochastic (Markov) game. However by using an additional condition, we have shown that a subclass of finite SeR-SIT-PT semi-Markov games have the ordered field property for both discounted and undiscounted semi-Markov games with both players having state-independent stationary optimals. The ordered field property also holds for the nonzero-sum case under the same assumptions. We find a relation between the values of the discounted and the undiscounted zero-sum semi-Markov games for this modified subclass. We propose a more realistic pollution tax model for this subclass of SeR-SIT semi-Markov games than pollution tax model for SeR-SIT stochastic game. Finite step algorithms are given for the discounted and for the zero-sum undiscounted cases.

Suggested Citation

  • Prasenjit Mondal & Sagnik Sinha, 2013. "Ordered Field Property In A Subclass Of Finite Ser-Sit Semi-Markov Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(04), pages 1-20.
    • Handle: RePEc:wsi:igtrxx:v:15:y:2013:i:04:n:s0219198913400264
    DOI: 10.1142/S0219198913400264
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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.
    2. Prasenjit Mondal, 2015. "Linear Programming and Zero-Sum Two-Person Undiscounted Semi-Markov Games," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(06), pages 1-20, December.

    More about this item

    Keywords

    Two-person semi-Markov games; discounted and undiscounted payoffs; minimax value and Nash equilibrium strategies; Archimedean ordered field property; semi-Markov games with separable reward and state-independent transition; 22E46; 53C35; 57S20;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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