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Nash equilibria in a class of Markov stopping games with total reward criterion

Author

Listed:
  • Rolando Cavazos-Cadena

    (Universidad Autónoma Agraria Antonio Narro)

  • Mario Cantú-Sifuentes

    (Universidad Autónoma Agraria Antonio Narro)

  • Imelda Cerda-Delgado

    (Universidad Autónoma Agraria Antonio Narro)

Abstract

This work is concerned with a class of discrete-time, zero-sum games with Markov transitions on a denumerable state space. At each decision time player II can stop the system paying a terminal reward to player I, or can let the system continue its evolution. If the system is not halted, player I selects an action which affects the transitions and receives a running reward from player II. The performance of a pair of decision strategies is measured by the total expected reward criterion and, under mild continuity-compactness conditions, communication-ergodicity properties are used to show that (i) the upper and lower value functions of the game coincide, and (ii) their common value is characterized as the unique fixed point of a nonexpansive operator from which a Nash equilibrium can be derived.

Suggested Citation

  • Rolando Cavazos-Cadena & Mario Cantú-Sifuentes & Imelda Cerda-Delgado, 2021. "Nash equilibria in a class of Markov stopping games with total reward criterion," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(2), pages 319-340, October.
    • Handle: RePEc:spr:mathme:v:94:y:2021:i:2:d:10.1007_s00186-021-00759-5
    DOI: 10.1007/s00186-021-00759-5
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    References listed on IDEAS

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    1. Douglas J. White, 1985. "Real Applications of Markov Decision Processes," Interfaces, INFORMS, vol. 15(6), pages 73-83, December.
    2. D. J. White, 1988. "Further Real Applications of Markov Decision Processes," Interfaces, INFORMS, vol. 18(5), pages 55-61, October.
    3. Ramsey, David M. & Szajowski, Krzysztof, 2008. "Selection of a correlated equilibrium in Markov stopping games," European Journal of Operational Research, Elsevier, vol. 184(1), pages 185-206, January.
    4. Nicole Bäuerle & Ulrich Rieder, 2014. "More Risk-Sensitive Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 39(1), pages 105-120, February.
    5. Goran Peskir, 2005. "On The American Option Problem," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 169-181, January.
    6. Tomasz Bielecki & Daniel Hernández-Hernández & Stanley R. Pliska, 1999. "Risk sensitive control of finite state Markov chains in discrete time, with applications to portfolio management," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(2), pages 167-188, October.
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    Cited by:

    1. Wenzhao Zhang & Congying Liu, 2024. "Discrete-time stopping games with risk-sensitive discounted cost criterion," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 100(2), pages 437-466, October.

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