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Deterministic Multi-Player Dynkin Games

  • Eilon Solan
  • Nicolas Vielle

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 one. We prove that a subgame-perfect e-equilibrium in Markovian strategies exists. If the game is not degenerate this e-equilibrium is actually in pure strategies.

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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1355.

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Date of creation: Sep 2002
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Handle: RePEc:nwu:cmsems:1355
Contact details of provider: Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014
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Web page: http://www.kellogg.northwestern.edu/research/math/
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  1. 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.
  2. 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.
  3. Eilon Solan & Dinah Rosenberg & Nicolas Vieille, 2001. "On the Max Min Value of Stochastic Games with Imperfect Monitoring," Discussion Papers 1337, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. 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.
  5. Brams, Steven J. & Kilgour, D. Mark, 1997. "The Truel," Working Papers 97-05, C.V. Starr Center for Applied Economics, New York University.
  6. Fine, Charles H. & Li, Lode, 1989. "Equilibrium exit in stochastically declining industries," Games and Economic Behavior, Elsevier, vol. 1(1), pages 40-59, March.
  7. VIEILLE, Nicolas & SOLAN, Eilon, 2001. "Quitting games - an example," Les Cahiers de Recherche 747, HEC Paris.
  8. Mertens, J.-F., 1986. "Repeated games," CORE Discussion Papers 1986024, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Eilon Solan & Nicolas Vieille, 1998. "Quitting Games," Discussion Papers 1227, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. 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.
  11. Solan, Eilon & Vieille, Nicolas, 2001. "Quitting Games," Economics Papers from University Paris Dauphine 123456789/6017, Paris Dauphine University.
  12. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, June.
  13. Janos Flesch & Frank Thuijsman & Koos Vrieze, 1997. "Cyclic Markov Equilibria in Stochastic Games," International Journal of Game Theory, Springer, vol. 26(3), pages 303-314.
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