IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v130y2020i11p6901-6926.html
   My bibliography  Save this article

Discontinuous Nash equilibrium points for nonzero-sum stochastic differential games

Author

Listed:
  • Hamadène, Said
  • Mu, Rui

Abstract

In this paper, we study a nonzero-sum stochastic differential game in the Markovian framework. We show the existence of a discontinuous Nash equilibrium point for this game. The main tool is the notion of backward stochastic differential equations which, in our case, are multidimensional with discontinuous generators with respect to z component.

Suggested Citation

  • Hamadène, Said & Mu, Rui, 2020. "Discontinuous Nash equilibrium points for nonzero-sum stochastic differential games," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6901-6926.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:11:p:6901-6926
    DOI: 10.1016/j.spa.2020.07.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414920303148
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2020.07.003?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. El-Karoui, N. & Hamadène, S., 2003. "BSDEs and risk-sensitive control, zero-sum and nonzero-sum game problems of stochastic functional differential equations," Stochastic Processes and their Applications, Elsevier, vol. 107(1), pages 145-169, September.
    2. Pierre Cardaliaguet & Slawomir Plaskacz, 2003. "Existence and uniqueness of a Nash equilibrium feedback for a simple nonzero-sum differential game," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(1), pages 33-71, December.
    3. Jia, Guangyan, 2008. "A class of backward stochastic differential equations with discontinuous coefficients," Statistics & Probability Letters, Elsevier, vol. 78(3), pages 231-237, February.
    4. A. Bensoussan & J. Frehse, 2000. "Stochastic Games for N Players," Journal of Optimization Theory and Applications, Springer, vol. 105(3), pages 543-565, June.
    5. Paola Mannucci, 2014. "Nash Points for Nonzero-Sum Stochastic Differential Games with Separate Hamiltonians," Dynamic Games and Applications, Springer, vol. 4(3), pages 329-344, September.
    6. Lepeltier, J. P. & San Martin, J., 1997. "Backward stochastic differential equations with continuous coefficient," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 425-430, April.
    7. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    8. Lin, Qian, 2015. "Nash equilibrium payoffs for stochastic differential games with jumps and coupled nonlinear cost functionals," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4405-4454.
    9. Fan, ShengJun & Jiang, Long, 2012. "One-dimensional BSDEs with left-continuous, lower semi-continuous and linear-growth generators," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1792-1798.
    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. Hu, Zuopeng & Yang, Yanlong, 2024. "Existence and generic stability of open-loop Nash equilibria for noncooperative fuzzy differential games," Applied Mathematics and Computation, Elsevier, vol. 463(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. Fan, ShengJun, 2016. "Existence of solutions to one-dimensional BSDEs with semi-linear growth and general growth generators," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 7-15.
    2. Xing, Hao & Žitković, Gordan, 2018. "A class of globally solvable Markovian quadratic BSDE systems and applications," LSE Research Online Documents on Economics 73440, London School of Economics and Political Science, LSE Library.
    3. Sheng Jun Fan, 2018. "Existence, Uniqueness and Stability of $$L^1$$ L 1 Solutions for Multidimensional Backward Stochastic Differential Equations with Generators of One-Sided Osgood Type," Journal of Theoretical Probability, Springer, vol. 31(3), pages 1860-1899, September.
    4. Fan, ShengJun, 2016. "Bounded solutions, Lp(p>1) solutions and L1 solutions for one dimensional BSDEs under general assumptions," Stochastic Processes and their Applications, Elsevier, vol. 126(5), pages 1511-1552.
    5. Fan, ShengJun & Jiang, Long, 2012. "One-dimensional BSDEs with left-continuous, lower semi-continuous and linear-growth generators," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1792-1798.
    6. Tian, Dejian & Jiang, Long & Davison, Matt, 2010. "On the existence of solutions to BSDEs with generalized uniformly continuous generators," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 903-909, May.
    7. R. Buckdahn & P. Cardaliaguet & M. Quincampoix, 2011. "Some Recent Aspects of Differential Game Theory," Dynamic Games and Applications, Springer, vol. 1(1), pages 74-114, March.
    8. Luis Escauriaza & Daniel C. Schwarz & Hao Xing, 2020. "Radner equilibrium and systems of quadratic BSDEs with discontinuous generators," Papers 2008.03500, arXiv.org, revised May 2021.
    9. Hamadène, S. & Wang, H., 2009. "BSDEs with two RCLL reflecting obstacles driven by Brownian motion and Poisson measure and a related mixed zero-sum game," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2881-2912, September.
    10. Said Hamadène & Rui Mu, 2021. "Risk-Sensitive Nonzero-Sum Stochastic Differential Game with Unbounded Coefficients," Dynamic Games and Applications, Springer, vol. 11(1), pages 84-108, March.
    11. Cao, Guilan & He, Kai, 2007. "Successive approximation of infinite dimensional semilinear backward stochastic evolution equations with jumps," Stochastic Processes and their Applications, Elsevier, vol. 117(9), pages 1251-1264, September.
    12. Bahlali, Khaled & Hamadène, SaI¨d & Mezerdi, Brahim, 2005. "Backward stochastic differential equations with two reflecting barriers and continuous with quadratic growth coefficient," Stochastic Processes and their Applications, Elsevier, vol. 115(7), pages 1107-1129, July.
    13. Qi Zhang & Huaizhong Zhao, 2012. "Probabilistic Representation of Weak Solutions of Partial Differential Equations with Polynomial Growth Coefficients," Journal of Theoretical Probability, Springer, vol. 25(2), pages 396-423, June.
    14. Zhou, Qing & Ren, Yong, 2012. "Reflected backward stochastic differential equations with time delayed generators," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 979-990.
    15. Djordjević, Jasmina & Janković, Svetlana, 2015. "Backward stochastic Volterra integral equations with additive perturbations," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 903-910.
    16. Tian, Dejian & Jiang, Long & Shi, Xuejun, 2013. "Lp solutions to backward stochastic differential equations with discontinuous generators," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 503-510.
    17. Monique Jeanblanc & Thibaut Mastrolia & Dylan Possamaï & Anthony Réveillac, 2015. "Utility Maximization With Random Horizon: A Bsde Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(07), pages 1-43, November.
    18. Paola Mannucci, 2014. "Nash Points for Nonzero-Sum Stochastic Differential Games with Separate Hamiltonians," Dynamic Games and Applications, Springer, vol. 4(3), pages 329-344, September.
    19. Fan, Shengjun & Hu, Ying, 2021. "Well-posedness of scalar BSDEs with sub-quadratic generators and related PDEs," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 21-50.
    20. Bayraktar, Erhan & Yao, Song, 2012. "Quadratic reflected BSDEs with unbounded obstacles," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1155-1203.

    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:11:p:6901-6926. 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.