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. repec:dau:papers:123456789/6927 is not listed on IDEAS
    2. 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.
    3. 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.
    4. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    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. 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).
    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.

    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. 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.
    4. 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.
    5. 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.
    6. Pablo Moran, 2017. "Information Revelation in Merger Waves," The Review of Corporate Finance Studies, Society for Financial Studies, vol. 6(2), pages 174-233.
    7. Paolo M. Panteghini & Michele Moretto, 2007. "Preemption, Start-Up Decisions and the Firms' Capital Structure," Economics Bulletin, AccessEcon, vol. 4(39), pages 1-14.
    8. Gianni De Fraja & Jozsef Sakovics, 2001. "Walras Retrouve: Decentralized Trading Mechanisms and the Competitive Price," Journal of Political Economy, University of Chicago Press, vol. 109(4), pages 842-863, August.
    9. Yu, Jing & Xu, Bin, 2011. "The game analyses to price the target enterprise of merger and acquisition based on the perspective of real options under stochastic surroundings," Economic Modelling, Elsevier, vol. 28(4), pages 1587-1594, July.
    10. Mark Isaac & Svetlana Pevnitskaya & Kurt S. Schnier, 2012. "Individual Behavior And Bidding Heterogeneity In Sealed Bid Auctions Where The Number Of Bidders Is Unknown," Economic Inquiry, Western Economic Association International, vol. 50(2), pages 516-533, April.
    11. Flavio Menezes & Paulo Klinger Monteiro, 1996. "A Note on Auctions with Endogenous Participation," Microeconomics 9610003, University Library of Munich, Germany, revised 31 Oct 1996.
    12. Bos, Olivier, 2012. "Wars of attrition and all-pay auctions with stochastic competition," Journal of Mathematical Economics, Elsevier, vol. 48(2), pages 83-91.
    13. Hsueh, Shao-Chieh & Tian, Guoqiang, 2009. "Nonratifiability of the Cartel Mechanism in First-Price Sealed-Bid Auction with Participation Costs," MPRA Paper 41202, University Library of Munich, Germany, revised Oct 2010.
    14. Tetsuya Kasahara, 2015. "Strategic Technology Adoption Under Dispersed Information and Information Learning," International Journal of Innovation and Technology Management (IJITM), World Scientific Publishing Co. Pte. Ltd., vol. 12(06), pages 1-18, December.
    15. Femminis, Gianluca & Martini, Gianmaria, 2011. "Irreversible investment and R&D spillovers in a dynamic duopoly," Journal of Economic Dynamics and Control, Elsevier, vol. 35(7), pages 1061-1090, July.
    16. Aytekin GÜVEN & Arzu AKKOYUNLU-WIGLEY, 2018. "The Effects of Market Structure on Uncertainty-Investment Relationship: Evidence from Turkish Manufacturing Industry," Sosyoekonomi Journal, Sosyoekonomi Society, issue 26(37).
    17. Mikhail Drugov & Dmitry Ryvkin, 2019. "The shape of luck and competition in tournaments," Working Papers w0251, Center for Economic and Financial Research (CEFIR).
    18. Ronald M. Harstad, 2005. "Rational Participation Revolutionizes Auction Theory," Working Papers 0518, Department of Economics, University of Missouri.
    19. Steven R. Grenadier, 2003. "An Equilibrium Analysis of Real Estate," NBER Working Papers 9475, National Bureau of Economic Research, Inc.
    20. Simon Grant & Atsushi Kajii & Flavio Menezes & Matthew J. Ryan, 2006. "Auctions with options to re‐auction," International Journal of Economic Theory, The International Society for Economic Theory, vol. 2(1), pages 17-39, March.

    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.