IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v130y2020i10p6133-6156.html
   My bibliography  Save this article

Playing with ghosts in a Dynkin game

Author

Listed:
  • De Angelis, Tiziano
  • Ekström, Erik

Abstract

We study a class of two-player optimal stopping games (Dynkin games) of preemption type, with uncertainty about the existence of competitors. The set-up is well-suited to model, for example, real options in the context of investors who do not want to publicly reveal their interest in a certain business opportunity. We show that if the underlying process is a Rd-valued, continuous, strong Markov process, and the stopping payoff is a continuous function (with mild integrability properties) there exists a Nash equilibrium in randomised stopping times for the game. Moreover, the equilibrium strategies and the expected payoffs of the two players are computed explicitly in terms of the corresponding one-player game. To the best of our knowledge this is the first paper to address this version of Dynkin games.

Suggested Citation

  • De Angelis, Tiziano & Ekström, Erik, 2020. "Playing with ghosts in a Dynkin game," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6133-6156.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:10:p:6133-6156
    DOI: 10.1016/j.spa.2020.05.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414919304387
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2020.05.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. McAfee, R. Preston & McMillan, John, 1987. "Auctions with a stochastic number of bidders," Journal of Economic Theory, Elsevier, vol. 43(1), pages 1-19, October.
    2. Touzi, N. & Vieille, N., 1999. "Continuous-Time Dynkin Games with Mixed Strategies," Papiers d'Economie Mathématique et Applications 1999.112, Université Panthéon-Sorbonne (Paris 1).
    3. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    4. repec:dau:papers:123456789/6927 is not listed on IDEAS
    5. Lambrecht, Bart & Perraudin, William, 2003. "Real options and preemption under incomplete information," Journal of Economic Dynamics and Control, Elsevier, vol. 27(4), pages 619-643, February.
    6. Harstad, Ronald M. & Kagel, John H. & Levin, Dan, 1990. "Equilibrium bid functions for auctions with an uncertain number of bidders," Economics Letters, Elsevier, vol. 33(1), pages 35-40, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. H. Dharma Kwon & Jan Palczewski, 2022. "Exit game with private information," Papers 2210.01610, arXiv.org, revised Oct 2023.
    2. Bodnariu, Andi & Lindensjö, Kristoffer, 2024. "A controller-stopper-game with hidden controller type," Stochastic Processes and their Applications, Elsevier, vol. 173(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tiziano De Angelis & Erik Ekstrom, 2019. "Playing with ghosts in a Dynkin game," Papers 1905.06564, arXiv.org.
    2. Boyarchenko, Svetlana & Levendorskiĭ, Sergei, 2014. "Preemption games under Lévy uncertainty," Games and Economic Behavior, Elsevier, vol. 88(C), pages 354-380.
    3. Yusuke Matsuki, 2016. "A Distribution-Free Test of Monotonicity with an Application to Auctions," Working Papers e110, Tokyo Center for Economic Research.
    4. Boyer, Marcel & Lasserre, Pierre & Moreaux, Michel, 2012. "A dynamic duopoly investment game without commitment under uncertain market expansion," International Journal of Industrial Organization, Elsevier, vol. 30(6), pages 663-681.
    5. Demetri Tsanacas, 2022. "Valuation Challenges in High Tech Platform Based Corporations," International Journal of Economics & Business Administration (IJEBA), International Journal of Economics & Business Administration (IJEBA), vol. 0(1), pages 89-100.
    6. Agliardi, Elettra & Andergassen, Rainer, 2009. "Last resort gambles, risky debt and liquidation policy," Review of Financial Economics, Elsevier, vol. 18(3), pages 142-155, August.
    7. Jeon, Haejun, 2015. "Patent infringement, litigation, and settlement," Economic Modelling, Elsevier, vol. 51(C), pages 99-111.
    8. Cesare Dosi & Michele Moretto, 2010. "Environmental Innovation, War Of Attrition And Investment Grants," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 12(01), pages 37-59.
    9. Edouard Civel & Marc Baudry, 2018. "The Fate of Inventions. What can we learn from Bayesian learning in strategic options model of adoption ?," EconomiX Working Papers 2018-47, University of Paris Nanterre, EconomiX.
    10. Thijssen, Jacco J. J. & Huisman, Kuno J. M. & Kort, Peter M., 2004. "The effect of information streams on capital budgeting decisions," European Journal of Operational Research, Elsevier, vol. 157(3), pages 759-774, September.
    11. Boosey, Luke & Brookins, Philip & Ryvkin, Dmitry, 2019. "Contests between groups of unknown size," Games and Economic Behavior, Elsevier, vol. 113(C), pages 756-769.
    12. Pawlina, Grzegorz & Kort, Peter M., 2005. "Investment under uncertainty and policy change," Journal of Economic Dynamics and Control, Elsevier, vol. 29(7), pages 1193-1209, July.
    13. Michele Moretto & Cesare Dosi, 2010. "Licences, "Use or Lose" Provisions and the Time of Investment," Working Papers 2010.24, Fondazione Eni Enrico Mattei.
    14. Bruno Versaevel, 2015. "Alertness, Leadership, and Nascent Market Dynamics," Dynamic Games and Applications, Springer, vol. 5(4), pages 440-466, December.
    15. Boosey, Luke & Brookins, Philip & Ryvkin, Dmitry, 2017. "Contests with group size uncertainty: Experimental evidence," Games and Economic Behavior, Elsevier, vol. 105(C), pages 212-229.
    16. Bolton, Patrick & Wang, Neng & Yang, Jinqiang, 2019. "Investment under uncertainty with financial constraints," Journal of Economic Theory, Elsevier, vol. 184(C).
    17. Milchtaich, Igal, 2004. "Random-player games," Games and Economic Behavior, Elsevier, vol. 47(2), pages 353-388, May.
    18. Pablo Moran, 2017. "Information Revelation in Merger Waves," The Review of Corporate Finance Studies, Society for Financial Studies, vol. 6(2), pages 174-233.
    19. Paolo M. Panteghini & Michele Moretto, 2007. "Preemption, Start-Up Decisions and the Firms' Capital Structure," Economics Bulletin, AccessEcon, vol. 4(39), pages 1-14.
    20. Vleugels, Jan, 1997. "Bidding against an unknown number of competitors sharing affiliated information," Papers 97-13, Sonderforschungsbreich 504.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:130:y:2020:i:10:p:6133-6156. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.