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Deterministic Multi-Player Dynkin Games

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  • Eilon Solan
  • Nicolas Vielle

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 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

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  1. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2001. "On the MaxMin Value of Stochastic Games with Imperfect Monitoring," Discussion Papers 1344, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. 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.
  3. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
  4. Eilon Solan & Nicolas Vieille, 2002. "Quitting games - An example," Working Papers hal-00242995, HAL.
  5. Solan, Eilon & Vieille, Nicolas, 2001. "Quitting Games," Economics Papers from University Paris Dauphine 123456789/6017, Paris Dauphine University.
  6. 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.
  7. Mertens, J.-F., 1986. "Repeated games," CORE Discussion Papers 1986024, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. 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.
  9. Eilon Solan & Nicolas Vieille, 1998. "Quitting Games," Discussion Papers 1227, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. 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.
  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. 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.
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Cited by:
  1. Flesch János & Kuipers Jeroen & Mashiah-Yaakovi Ayala & Schoenmakers Gijs & Solan Eilon & Vrieze Koos, 2010. "Borel Games with Lower-Semi-Continuous Payoffs," Research Memorandum 040, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  2. Kuipers, Jeroen & Flesch, Janos & Schoenmakers, Gijs & Vrieze, Koos, 2008. "Pure Subgame-Perfect Equilibria in Free Transition Games," Research Memorandum 027, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  3. Ayala Mashiah-Yaakovi, 2009. "Periodic stopping games," International Journal of Game Theory, Springer, vol. 38(2), pages 169-181, June.
  4. Ayala Mashiah-Yaakovi, 2014. "Subgame perfect equilibria in stopping games," International Journal of Game Theory, Springer, vol. 43(1), pages 89-135, February.
  5. Flesch, János & Kuipers, Jeroen & Schoenmakers, Gijs & Vrieze, Koos, 2008. "Subgame-Perfection in Stochastic Games with Perfect Information and Recursive Payoffs," Research Memorandum 041, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  6. Yuri Kifer, 2012. "Dynkin Games and Israeli Options," Papers 1209.1791, arXiv.org.
  7. Flesch J. & Kuipers J. & Schoenmakers G. & Vrieze K., 2011. "Subgame-Perfection in Free Transition Games," Research Memorandum 047, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

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