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Some Recent Aspects of Differential Game Theory

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Listed author(s):
  • R. Buckdahn

    ()

  • P. Cardaliaguet

    ()

  • M. Quincampoix

    ()

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    Abstract

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    File URL: http://hdl.handle.net/10.1007/s13235-010-0005-0
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    Article provided by Springer in its journal Dynamic Games and Applications.

    Volume (Year): 1 (2011)
    Issue (Month): 1 (March)
    Pages: 74-114

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    Handle: RePEc:spr:dyngam:v:1:y:2011:i:1:p:74-114
    DOI: 10.1007/s13235-010-0005-0
    Contact details of provider: Web page: http://www.springer.com

    Order Information: Web: http://www.springer.com/economics/journal/13235

    Keywords: Differential game; Viscosity solution; System of Hamilton–Jacobi equations; Mean-field games; State-constraints; Backward stochastic differential equations; Incomplete information;

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    1. DE MEYER, Bernard & ROSENBERG, Dinah, 1997. "“Cav u” and the dual game," CORE Discussion Papers 1997048, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. 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.
    3. Gaitsgory, Vladimir & Nitzan, Shmuel, 1994. "A folk theorem for dynamic games," Journal of Mathematical Economics, Elsevier, vol. 23(2), pages 167-178, March.
    4. repec:dau:papers:123456789/6927 is not listed on IDEAS
    5. 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.
    6. DE MEYER , Bernard, 1993. "Repeated Games and the Central Limit Theorem," CORE Discussion Papers 1993003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Buckdahn, Rainer & Li, Juan & Peng, Shige, 2009. "Mean-field backward stochastic differential equations and related partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3133-3154, October.
    8. P. Cardaliaguet & M. Quincampoix, 2008. "Deterministic Differential Games Under Probability Knowledge Of Initial Condition," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(01), pages 1-16.
    9. Alberto Bressan & Wen Shen, 2004. "Semi-cooperative strategies for differential games," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(4), pages 561-593, 08.
    10. Philippe Robert-Demontrond & R. Ringoot, 2004. "Introduction," Post-Print halshs-00081823, HAL.
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    Cited by:

    1. Rainer Buckdahn & Marc Quincampoix & Catherine Rainer & Yuhong Xu, 2016. "Differential games with asymmetric information and without Isaacs’ condition," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 795-816, November.
    2. Alessandra Buratto & Luca Grosset & Bruno Viscolani, 2012. "ε-Subgame Perfectness of an Open-Loop Stackelberg Equilibrium in Linear-State Games," Dynamic Games and Applications, Springer, vol. 2(3), pages 269-279, September.
    3. Rainer Buckdahn & Juan Li & Marc Quincampoix, 2013. "Value function of differential games without Isaacs conditions. An approach with nonanticipative mixed strategies," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 989-1020, November.
    4. Minyi Huang, 2013. "A Mean Field Capital Accumulation Game with HARA Utility," Dynamic Games and Applications, Springer, vol. 3(4), pages 446-472, December.
    5. Chloe Jimenez & Marc Quincampoix & Yuhong Xu, 2016. "Differential Games with Incomplete Information on a Continuum of Initial Positions and without Isaacs Condition," Dynamic Games and Applications, Springer, vol. 6(1), pages 82-96, March.
    6. Boualem Djehiche & Minyi Huang, 2016. "A Characterization of Sub-game Perfect Equilibria for SDEs of Mean-Field Type," Dynamic Games and Applications, Springer, vol. 6(1), pages 55-81, March.
    7. 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.
    8. E. N. Barron, 2017. "Differential Games in $$L^{\infty }$$ L ∞," Dynamic Games and Applications, Springer, vol. 7(2), pages 157-184, June.

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