Previous article Next article Nash Equilibrium Payoffs for Nonzero-Sum Stochastic Differential GamesRainer Buckdahn, Pierre Cardaliaguet, and Catherine RainerRainer Buckdahn, Pierre Cardaliaguet, and Catherine Rainerhttps://doi.org/10.1137/S0363012902411556PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractExistence and characterization of Nash equilibrium payoffs are proved for stochastic nonzero-sum differential games.[1] A. Bensoussan and , J. Frehse, Stochastic games for N players, J. Optim. Theory Appl., 105 (2000), 543–565, Special Issue in honor of Professor David G. Luenberger 10.1023/A:1004637022496 2002g:49049 CrossrefISIGoogle Scholar[2] W. Fleming and , P. Souganidis, On the existence of value functions of two‐player, zero‐sum stochastic differential games, Indiana Univ. Math. J., 38 (1989), 293–314 90e:93089 CrossrefISIGoogle Scholar[3] S. Hamadene, , J.‐P. Lepeltier and , S. 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Appl., 119 (1986), 182–202 88d:90144 CrossrefISIGoogle ScholarKeywordsnonzero-sum differential gamestochastic differential gameNash equilibrium Previous article Next article FiguresRelatedReferencesCited byDetails A BSDE Approach to Stochastic Differential Games Involving Impulse Controls and HJBI Equation23 October 2021 | Journal of Systems Science and Complexity, Vol. 35, No. 3 Cross Ref State and Control Path-Dependent Stochastic Zero-Sum Differential Games: Viscosity Solutions of Path-Dependent Hamilton–Jacobi–Isaacs Equations22 May 2022 | Mathematics, Vol. 10, No. 10 Cross Ref Competition and equilibrium effort choiceJournal of Economic Dynamics and Control, Vol. 137 Cross Ref Dynamic Set Values for Nonzero-Sum Games with Multiple EquilibriumsMathematics of Operations Research, Vol. 47, No. 1 Cross Ref Dynamic Equilibrium of Market Making with Price Competition10 December 2020 | Dynamic Games and Applications, Vol. 11, No. 3 Cross Ref Maximum Principle for Non-Zero Sum Stochastic Differential Game with Discrete and Distributed Delays9 September 2020 | Journal of Systems Science and Complexity, Vol. 34, No. 2 Cross Ref Discontinuous Nash equilibrium points for nonzero-sum stochastic differential gamesStochastic Processes and their Applications, Vol. 130, No. 11 Cross Ref Linear–quadratic mean field stochastic zero-sum differential gamesAutomatica, Vol. 120 Cross Ref Explicit Characterization of Feedback Nash Equilibria for Indefinite, Linear-Quadratic, Mean-Field-Type Stochastic Zero-Sum Differential Games with Jump-Diffusion Models28 September 2020 | Mathematics, Vol. 8, No. 10 Cross Ref An example of multiple mean field limits in ergodic differential games9 April 2020 | Nonlinear Differential Equations and Applications NoDEA, Vol. 27, No. 3 Cross Ref Nonzero-Sum Stochastic Differential Games with Impulse Controls: A Verification Theorem with ApplicationsMathematics of Operations Research, Vol. 45, No. 1 Cross Ref Nonzero-Sum Submodular Monotone-Follower Games: Existence and Approximation of Nash EquilibriaJodi Dianetti and Giorgio Ferrari7 May 2020 | SIAM Journal on Control and Optimization, Vol. 58, No. 3AbstractPDF (615 KB)Differential Games21 August 2020 Cross Ref Nash Tracking Game with Preview by State Feedback for Linear Continuous-Time SystemsProceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications, Vol. 2019, No. 0 Cross Ref Nash Tracking Game with Preview by State Feedback for Linear Continuous-Time Markovian Jump SystemsProceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications, Vol. 2019, No. 0 Cross Ref A Zero-Sum Stochastic Differential Game with Impulses, Precommitment, and Unrestricted Cost Functions29 August 2017 | Applied Mathematics & Optimization, Vol. 79, No. 2 Cross Ref Linear–quadratic stochastic two-person nonzero-sum differential games: Open-loop and closed-loop Nash equilibriaStochastic Processes and their Applications, Vol. 129, No. 2 Cross Ref Nash equilibrium payoffs for non-zero-sum stochastic differential games without Isaacs condition22 July 2018 | Stochastics, Vol. 91, No. 1 Cross Ref Approximate Public-Signal Correlated Equilibria for Nonzero-Sum Differential GamesYurii Averboukh21 February 2019 | SIAM Journal on Control and Optimization, Vol. 57, No. 1AbstractPDF (567 KB)On the (In)efficiency of MFG EquilibriaPierre Cardaliaguet and Catherine Rainer9 July 2019 | SIAM Journal on Control and Optimization, Vol. 57, No. 4AbstractPDF (483 KB)Soft-Constrained Nash Tracking Game with Preview by State Feedback for Linear Continuous-Time Markovian Jump Systems Cross Ref Differential Games25 September 2019 Cross Ref BSDES in games, coupled with the value functions. associated nonlocal Bellman-Isaacs equationsActa Mathematica Scientia, Vol. 37, No. 5 Cross Ref Zero-sum and nonzero-sum differential games without Isaacs condition12 May 2017 | ESAIM: Control, Optimisation and Calculus of Variations, Vol. 23, No. 3 Cross Ref Existence of game value and approximating Nash equilibrium for path-dependent stochastic differential game Cross Ref TUG-OF-WAR, MARKET MANIPULATION, AND OPTION PRICING18 December 2014 | Mathematical Finance, Vol. 27, No. 2 Cross Ref The Existence of Game Value for Path-dependent Stochastic Differential GameFu Zhang17 August 2017 | SIAM Journal on Control and Optimization, Vol. 55, No. 4AbstractPDF (361 KB)Finite horizon linear quadratic dynamic games for discrete-time stochastic systems with N -playersOperations Research Letters, Vol. 44, No. 3 Cross Ref Non-zero sum quadratic differential game of BSDEs and multi-dimensional diagonally quadratic BSDE**This research was supported by the National Natural Science Foundation of China (Grants #10325101 and #11171076), by Science and Technology Commission, Shanghai Municipality (Grant No. 14XD1400400), and by Lebesgue center of mathematics ("Investisse-ments d'avenir" program - 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Kushner28 November 2007 | SIAM Journal on Control and Optimization, Vol. 46, No. 6AbstractPDF (335 KB) Volume 43, Issue 2| 2004SIAM Journal on Control and Optimization History Published online:26 July 2006 InformationCopyright © 2004 Society for Industrial and Applied MathematicsKeywordsnonzero-sum differential gamestochastic differential gameNash equilibriumMSC codes91A2391A15PDF Download Article & Publication DataArticle DOI:10.1137/S0363012902411556Article page range:pp. 624-642ISSN (print):0363-0129ISSN (online):1095-7138Publisher:Society for Industrial and Applied Mathematics
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