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Stopping Games with Randomized Strategies

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  • Dinah Rosenberg
  • Eilon Solan
  • Nicolas Vieille

Abstract

We study stopping games in the setup of Neveu. We prove the existence of a uniform value (in a sense defined below), by allowing the players to use randomized strategies. In contrast with previous work, we make no comparison assumption on the payoff processes. Moreover, we prove that the value is the limit of discounted values, and we construct e-optimal strategies.

Suggested Citation

  • 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.
  • Handle: RePEc:nwu:cmsems:1258
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    File URL: http://www.kellogg.northwestern.edu/research/math/papers/1258.pdf
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    References listed on IDEAS

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    1. Mertens, Jean-Francois, 2002. "Stochastic games," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 47, pages 1809-1832 Elsevier.
    2. Yasuda, M., 1985. "On a randomized strategy in Neveu's stopping problem," Stochastic Processes and their Applications, Elsevier, vol. 21(1), pages 159-166, December.
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    Cited by:

    1. Solan, Eilon & Vieille, Nicolas, 2003. "Deterministic multi-player Dynkin games," Journal of Mathematical Economics, Elsevier, vol. 39(8), pages 911-929, November.
    2. Shmaya, Eran & Solan, Eilon & Vieille, Nicolas, 2003. "An application of Ramsey theorem to stopping games," Games and Economic Behavior, Elsevier, vol. 42(2), pages 300-306, February.
    3. Eilon Solan & Nicolas Vieille, 2001. "Stopping Games: recent results," Working Papers hal-00595484, HAL.
    4. 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.
    5. Gechun Liang & Haodong Sun, 2018. "Dynkin games with Poisson random intervention times," Papers 1803.00329, arXiv.org.
    6. Eilon Solan & Nicolas Vieille, 2000. "Uniform Value in Recursive Games," Discussion Papers 1293, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. Yuri Kifer, 2012. "Dynkin Games and Israeli Options," Papers 1209.1791, arXiv.org.
    8. Sandroni, Alvaro & Urgun, Can, 2017. "Dynamics in Art of War," Mathematical Social Sciences, Elsevier, vol. 86(C), pages 51-58.
    9. Shmaya, Eran & Solan, Eilon, 2004. "Zero-sum dynamic games and a stochastic variation of Ramsey's theorem," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 319-329, August.
    10. Rida Laraki & Eilon Solan, 2002. "Stopping Games in Continuous Time," Discussion Papers 1354, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    11. Erhan Bayraktar & Song Yao, 2015. "On the Robust Dynkin Game," Papers 1506.09184, arXiv.org, revised Sep 2016.
    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.
    13. Rida Laraki & Eilon Solan, 2012. "Equilibrium in Two-Player Nonzero-Sum Dynkin Games in Continuous Time," Working Papers hal-00753508, HAL.
    14. Ayala Mashiah-Yaakovi, 2009. "Periodic stopping games," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(2), pages 169-181, June.
    15. Eran Schmaya & Eilon Solan & Nicolas Vieille, 2002. "Stopping games and Ramsey theorem," Working Papers hal-00242997, HAL.
    16. Eilon Solan, 2005. "Subgame-Perfection in Quitting Games with Perfect Information and Differential Equations," Mathematics of Operations Research, INFORMS, vol. 30(1), pages 51-72, February.
    17. Zhou Zhou, 2015. "Non-zero-sum stopping games in discrete time," Papers 1508.06032, arXiv.org.
    18. Michael Ludkovski, 2010. "Stochastic Switching Games and Duopolistic Competition in Emissions Markets," Papers 1001.3455, arXiv.org, revised Aug 2010.
    19. Guo, Ivan & Rutkowski, Marek, 2016. "Discrete time stochastic multi-player competitive games with affine payoffs," Stochastic Processes and their Applications, Elsevier, vol. 126(1), pages 1-32.

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