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Deterministic multi-player Dynkin games

Author

Listed:
  • Nicolas Vieille

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

  • Eilon Solan

    (TAU - Tel Aviv University)

Abstract

A multi-player Dynkin game is a sequential game in which at every stage one of the players is chosen, and that player can decide whether to continue the game or to stop it, in which case all players receive some terminal payoff. We study a variant of this model, where the order by which players are chosen is deterministic, and the probability that the game terminates once the chosen player decides to stop may be strictly less than 1. We prove that a subgame-perfect ε-equilibrium in Markovian strategies exists. If the game is not degenerate this ε-equilibrium is actually in pure strategies.

Suggested Citation

  • Nicolas Vieille & Eilon Solan, 2003. "Deterministic multi-player Dynkin games," Post-Print hal-00464953, HAL.
    • Handle: RePEc:hal:journl:hal-00464953
    DOI: 10.1016/S0304-4068(03)00021-1
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    References listed on IDEAS

    as
    1. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2003. "The MaxMin value of stochastic games with imperfect monitoring," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(1), pages 133-150, December.
    2. MERTENS, Jean-François, 1987. "Repeated games. Proceedings of the International Congress of Mathematicians," LIDAM Reprints CORE 788, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Eilon Solan & Nicolas Vieille, 1998. "Quitting Games," Discussion Papers 1227, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2002. "Stochastic Games with Imperfect Monitoring," Discussion Papers 1341, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107030206.
      • Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107662636.
    6. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
    7. Eilon Solan, 2002. "Subgame-Perfection in Quitting Games with Perfect Information and Differential Equations," Discussion Papers 1356, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. Eilon Solan & Nicholas Vieille, 2001. "Quitting Games - An Example," Discussion Papers 1314, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    9. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 1999. "Stopping Games with Randomized Strategies," Discussion Papers 1258, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    10. repec:dau:papers:123456789/6017 is not listed on IDEAS
    11. Fine, Charles H. & Li, Lode, 1989. "Equilibrium exit in stochastically declining industries," Games and Economic Behavior, Elsevier, vol. 1(1), pages 40-59, March.
    12. Janos Flesch & Frank Thuijsman & Koos Vrieze, 1997. "Cyclic Markov Equilibria in Stochastic Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(3), pages 303-314.
    13. Eran Shmaya & Eilon Solan, 2002. "Two Player Non Zero-Sum Stopping Games in Discrete Time," Discussion Papers 1347, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    14. Brams, Steven J. & Kilgour, D. Mark, 1997. "The Truel," Working Papers 97-05, C.V. Starr Center for Applied Economics, New York University.
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    More about this item

    Keywords

    Dynkin game; Stochastic game; Equilibrium; n-player games;
    All these keywords.

    JEL classification:

    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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