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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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    2. 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.
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    6. Goran Peskir, 2005. "On The American Option Problem," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 169-181, January.
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