IDEAS home Printed from https://ideas.repec.org/a/spr/dyngam/v14y2024i3d10.1007_s13235-023-00500-3.html
   My bibliography  Save this article

$$\varepsilon $$ ε -Nash Equilibria of a Multi-player Nonzero-Sum Dynkin Game in Discrete Time

Author

Listed:
  • Said Hamadène

    (Le Mans Université, LMM)

  • Mohammed Hassani

    (Université Cadi Ayyad)

  • Marie-Amélie Morlais

    (Le Mans Université, LMM)

Abstract

We study the infinite horizon discrete time N-player nonzero-sum Dynkin game ( $$N\ge 2$$ N ≥ 2 ) with stopping times as strategies (or pure strategies). We prove existence of an $$\varepsilon $$ ε -Nash equilibrium point for the game by presenting a constructive algorithm. One of the main features is that the payoffs of the players depend on the set of players that stop at the termination stage which is the minimal stage in which at least one player stops. The existence result is extended to the case of a nonzero-sum game with finite horizon. Finally, the algorithm is illustrated by two explicit examples in the specific case of finite horizon.

Suggested Citation

  • Said Hamadène & Mohammed Hassani & Marie-Amélie Morlais, 2024. "$$\varepsilon $$ ε -Nash Equilibria of a Multi-player Nonzero-Sum Dynkin Game in Discrete Time," Dynamic Games and Applications, Springer, vol. 14(3), pages 642-664, July.
    • Handle: RePEc:spr:dyngam:v:14:y:2024:i:3:d:10.1007_s13235-023-00500-3
    DOI: 10.1007/s13235-023-00500-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13235-023-00500-3
    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/s13235-023-00500-3?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. Yuval Heller, 2012. "Sequential Correlated Equilibria in Stopping Games," Operations Research, INFORMS, vol. 60(1), pages 209-224, February.
    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. Yoshio Ohtsubo, 1987. "A Nonzero-Sum Extension of Dynkin's Stopping Problem," Mathematics of Operations Research, INFORMS, vol. 12(2), pages 277-296, May.
    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. Said Hamadène & Mohammed Hassani, 2014. "The multi-player nonzero-sum Dynkin game in discrete time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(2), pages 179-194, April.
    2. 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.
    3. 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.
    4. VIEILLE, Nicolas & SOLAN, Eilon, 2001. "Stopping games: recent results," HEC Research Papers Series 744, HEC Paris.
    5. Miryana Grigorova & Marie-Claire Quenez & Yuan Peng, 2023. "Non-linear non-zero-sum Dynkin games with Bermudan strategies," Papers 2311.01086, arXiv.org.
    6. Eilon Solan & Nicolas Vieille, 2001. "Quitting Games," Mathematics of Operations Research, INFORMS, vol. 26(2), pages 265-285, May.
    7. Sandroni, Alvaro & Urgun, Can, 2017. "Dynamics in Art of War," Mathematical Social Sciences, Elsevier, vol. 86(C), pages 51-58.
    8. Yu-Jui Huang & Zhou Zhou, 2021. "A Time-Inconsistent Dynkin Game: from Intra-personal to Inter-personal Equilibria," Papers 2101.00343, arXiv.org, revised Dec 2021.
    9. Anna Krasnosielska-Kobos, 2016. "Construction of Nash equilibrium based on multiple stopping problem in multi-person game," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 53-70, February.
    10. Anna Krasnosielska-Kobos, 2016. "Construction of Nash equilibrium based on multiple stopping problem in multi-person game," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 53-70, February.
    11. János Flesch & Arkadi Predtetchinski & William Sudderth, 2021. "Discrete stop-or-go games," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 559-579, June.
    12. Flesch, J. & Kuipers, J. & Schoenmakers, G. & Vrieze, K., 2008. "Subgame-perfection in stochastic games with perfect information and recursive payoffs," Research Memorandum 041, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    13. Said Hamadene & Jianfeng Zhang, 2008. "The Continuous Time Nonzero-sum Dynkin Game Problem and Application in Game Options," Papers 0810.5698, arXiv.org.
    14. 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.
    15. Yu-Jui Huang & Zhou Zhou, 2022. "A time-inconsistent Dynkin game: from intra-personal to inter-personal equilibria," Finance and Stochastics, Springer, vol. 26(2), pages 301-334, April.
    16. Eran Schmaya & Eilon Solan & Nicolas Vieille, 2002. "Stopping games and Ramsey theorem," Working Papers hal-00242997, HAL.
    17. Eilon Solan & Omri N. Solan, 2020. "Quitting Games and Linear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 434-454, May.
    18. J. Flesch & J. Kuipers & G. Schoenmakers & K. Vrieze, 2010. "Subgame Perfection in Positive Recursive Games with Perfect Information," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 193-207, February.
    19. Miryana Grigorova & Marie-Claire Quenez, 2017. "Optimal stopping and a non-zero-sum Dynkin game in discrete time with risk measures induced by BSDEs," Papers 1705.03724, arXiv.org.
    20. Nowak, Andrzej S. & Szajowski, Krzysztof, 1998. "Nonzero-sum Stochastic Games," MPRA Paper 19995, University Library of Munich, Germany, revised 1999.

    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:dyngam:v:14:y:2024:i:3:d:10.1007_s13235-023-00500-3. 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.