IDEAS home Printed from https://ideas.repec.org/b/spr/mathfi/v18y2024i2d10.1007_s11579-024-00367-x.html
   My bibliography  Save this book

On the value of a time-inconsistent mean-field zero-sum Dynkin game

Author

Listed:
  • Boualem Djehiche

    (KTH Royal Institute of Technology)

Abstract

We study a mean-field zero-sum Dynkin game (MF-ZSDG) with time-inconsistent performance functionals adapted to the Brownian filtration. Despite the time-inconsistency of the MF-ZSDG, we show that it admits a value and that the pair of first times the value process hits the upper and lower obstacles, respectively, is a saddle point for the game. We solve the problem by approximating the associated lower and upper value processes with a sequence of value processes of interacting time-consistent zero-sum Dynkin games for which the saddle point of each of the value processes is the pair of first times each of those value processes hits the associated upper and lower obstacles, respectively. Under mild assumptions, we show that this sequence of saddle points converges in probability to the pair of first hitting times of the value process of the upper and lower obstacles, respectively, and that the limit is a saddle point for the time-inconsistent MF-ZSDG.

Suggested Citation

  • Boualem Djehiche, 2024. "On the value of a time-inconsistent mean-field zero-sum Dynkin game," Mathematics and Financial Economics, Springer, volume 18, number 12.
    • Handle: RePEc:spr:mathfi:v:18:y:2024:i:2:d:10.1007_s11579-024-00367-x
    DOI: 10.1007/s11579-024-00367-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11579-024-00367-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11579-024-00367-x?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

    for a different version of it.

    References listed on IDEAS

    as
    1. 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).
    2. 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.
    3. 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.
    4. Wellner, Jon A., 1981. "A Glivenko-Cantelli theorem for empirical measures of independent but non-identically distributed random variables," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 309-312, August.
    Full references (including those not matched with items on IDEAS)

    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. Rida Laraki & Eilon Solan, 2012. "Equilibrium in Two-Player Nonzero-Sum Dynkin Games in Continuous Time," Working Papers hal-00753508, HAL.
    2. Yuri Kifer, 2012. "Dynkin Games and Israeli Options," Papers 1209.1791, arXiv.org.
    3. Gechun Liang & Haodong Sun, 2018. "Dynkin games with Poisson random intervention times," Papers 1803.00329, arXiv.org, revised Jul 2019.
    4. David Hobson & Gechun Liang & Edward Wang, 2021. "Callable convertible bonds under liquidity constraints and hybrid priorities," Papers 2111.02554, arXiv.org, revised Oct 2024.
    5. Steg, Jan-Henrik, 2018. "Preemptive investment under uncertainty," Games and Economic Behavior, Elsevier, vol. 110(C), pages 90-119.
    6. Riedel, Frank & Steg, Jan-Henrik, 2017. "Subgame-perfect equilibria in stochastic timing games," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 36-50.
    7. Vicky Henderson & David Hobson & Matthew Zeng, 2023. "Cautious stochastic choice, optimal stopping and deliberate randomization," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(3), pages 887-922, April.
    8. David Adams & Alan Disberry & Norman Hutchison & Thomas Munjoma, 2001. "Ownership Constraints to Brownfield Redevelopment," Environment and Planning A, , vol. 33(3), pages 453-477, March.
    9. Helen Weeds, 2002. "Strategic Delay in a Real Options Model of R&D Competition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(3), pages 729-747.
    10. Bonatti, Alessandro & Hörner, Johannes, 2017. "Learning to disagree in a game of experimentation," Journal of Economic Theory, Elsevier, vol. 169(C), pages 234-269.
    11. 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.
    12. Bulan, Laarni & Mayer, Christopher & Somerville, C. Tsuriel, 2009. "Irreversible investment, real options, and competition: Evidence from real estate development," Journal of Urban Economics, Elsevier, vol. 65(3), pages 237-251, May.
    13. Alet Roux, 2015. "Pricing and hedging game options in currency models with proportional transaction costs," Papers 1504.07920, arXiv.org, revised Aug 2015.
    14. Bustamante, Maria Cecilia, 2011. "Strategic investment, industry concentration and the cross section of returns," LSE Research Online Documents on Economics 37454, London School of Economics and Political Science, LSE Library.
    15. Chu, Yongqiang & Sing, Tien Foo, 2021. "Intensity and Timing Options in Real Estate Developments," International Real Estate Review, Global Social Science Institute, vol. 24(1), pages 1-17.
    16. Miss Mali Chivakul & Mr. Waikei Raphael Lam & Xiaoguang Liu & Wojciech Maliszewski & Mr. Alfred Schipke, 2015. "Understanding Residential Real Estate in China," IMF Working Papers 2015/084, International Monetary Fund.
    17. Rutger-Jan Lange & Coen N. Teulings, 2021. "The option value of vacant land: Don't build when demand for housing is booming," Tinbergen Institute Discussion Papers 21-022/IV, Tinbergen Institute.
    18. Doriana Ruffino & Jonathan Treussard, 2006. "Lumps and Clusters in Duopolistic Investment Games: An Early Exercise Premium Approach," Boston University - Department of Economics - Working Papers Series WP2006-044, Boston University - Department of Economics.
    19. Bouveret, Géraldine & Dumitrescu, Roxana & Tankov, Peter, 2022. "Technological change in water use: A mean-field game approach to optimal investment timing," Operations Research Perspectives, Elsevier, vol. 9(C).
    20. Siddiqui, Afzal & Takashima, Ryuta, 2012. "Capacity switching options under rivalry and uncertainty," European Journal of Operational Research, Elsevier, vol. 222(3), pages 583-595.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:spr:mathfi:v:18:y:2024:i:2:d:10.1007_s11579-024-00367-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.