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Equilibrium in Two-Player Nonzero-Sum Dynkin Games in Continuous Time

Author

Listed:
  • Rida Laraki

    (Ecole Polytechnique [Palaiseau], IMJ - Institut de Mathématiques de Jussieu - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

  • Eilon Solan

    () (School of Mathematical Sciences [Tel Aviv] - Raymond and Beverly Sackler Faculty of Exact Sciences - Tel Aviv University [Tel Aviv])

Abstract

We prove that every two-player nonzero-sum Dynkin game in continuous time admits an "epsilon" equilibrium in randomized stopping times. We provide a condition that ensures the existence of an "epsilon" equilibrium in nonrandomized stopping times.

Suggested Citation

  • Rida Laraki & Eilon Solan, 2012. "Equilibrium in Two-Player Nonzero-Sum Dynkin Games in Continuous Time," Working Papers hal-00753508, HAL.
  • Handle: RePEc:hal:wpaper:hal-00753508 Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00753508
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    File URL: https://hal.archives-ouvertes.fr/hal-00753508/document
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    References listed on IDEAS

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    1. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, January.
    2. 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.
    3. Laraki, Rida & Solan, Eilon & Vieille, Nicolas, 2005. "Continuous-time games of timing," Journal of Economic Theory, Elsevier, vol. 120(2), pages 206-238, February.
    4. Tomasz Bielecki & Stephane Crepey & Monique Jeanblanc & Marek Rutkowski, 2008. "Arbitrage pricing of defaultable game options with applications to convertible bonds," Quantitative Finance, Taylor & Francis Journals, vol. 8(8), pages 795-810.
    5. 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.
    6. Hendricks, Ken & Weiss, Andrew & Wilson, Charles A, 1988. "The War of Attrition in Continuous Time with Complete Information," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(4), pages 663-680, November.
    7. Grenadier, Steven R, 1996. " The Strategic Exercise of Options: Development Cascades and Overbuilding in Real Estate Markets," Journal of Finance, American Finance Association, vol. 51(5), pages 1653-1679, December.
    8. Rida Laraki & Eilon Solan, 2002. "Stopping Games in Continuous Time," Discussion Papers 1354, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    9. Yuri Kifer, 2000. "Game options," Finance and Stochastics, Springer, vol. 4(4), pages 443-463.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. 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.
    2. Nie, Tianyang & Rutkowski, Marek, 2014. "Multi-player stopping games with redistribution of payoffs and BSDEs with oblique reflection," Stochastic Processes and their Applications, Elsevier, vol. 124(8), pages 2672-2698.

    More about this item

    Keywords

    continuous time; Dynkin games; stopping games; equilibrium; stochastic analysis; continuous time.;

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