Open Access
Issue
ESAIM: COCV
Volume 30, 2024
Article Number 47
Number of page(s) 41
DOI https://doi.org/10.1051/cocv/2024037
Published online 11 June 2024
  1. L. Mou and J. Yong, Two-person zero-sum linear quadratic stochastic differential games by a Hilbert space method. J. Ind. Manag. Optim. 2 (2006) 95–117. [Google Scholar]
  2. J. Sun and J. Yong, Linear quadratic stochastic differential games: open-loop and closed-loop saddle points. SIAM J. Control Optim. 52 (2014) 4082–4121. [CrossRef] [MathSciNet] [Google Scholar]
  3. J. Sun and J. Yong, Linear-quadratic stochastic two-person nonzero-sum differential games: open-loop and closed-loop Nash equilibria. Stoch. Proc. Appl. 219 (2019) 381–418. [Google Scholar]
  4. Z. Yu, An optimal feedback control-strategy pair for zero-sum linear-quadratic stochastic differential game: the Riccati equation approach. SIAM J. Control Optim. 53 (2015) 2141–2167. [Google Scholar]
  5. S. Hamadène, Backward-forward SDE’s and stochastic differential games. Stoch. Proc. Appl. 77 (1998) 1–15. [Google Scholar]
  6. S. Hamadène, Nonzero sum linear-quadratic stochastic differential games and backward-forward equations. Stoch. Anal. Appl. 17 (1999) 117–130. [Google Scholar]
  7. W.H. Fleming and P.E. Souganidis, On the existence of value functions of two-player, zero-sum stochastic differential games. Indiana Univ. Math. J. 38 (1989) 293–314. [Google Scholar]
  8. R. Buckdahn, P. Cardaliaguet and C. Rainer, Nash equilibrium payoffs for nonzero-sum stochastic differential games. SIAM J. Control Optim. 43 (2004) 624–642. [Google Scholar]
  9. R. Buckdahn and J. Li, Stochastic differential games and viscosity solutions of Hamilton–Jacobi–Bellman–Isaacs equations. SIAM J. Control Optim. 47 (2008) 444–475. [Google Scholar]
  10. H. von Stackelberg. The Theory of the Market Economy. Oxford University, New York (1952). [Google Scholar]
  11. T. Basar and G.J. Olsder, Dynamic Noncooperative Game Theory. Classics Appl. Math. SIAM, Philadelphia (1999). [Google Scholar]
  12. N.V. Long, A Survey of Dynamic Games in Economics. World Scientific, Singapore (2010). [Google Scholar]
  13. J. Yong, A leader-follower stochastic linear quadratic differential game. SIAM J. Control Optim. 41 (2002) 1015–1041. [CrossRef] [MathSciNet] [Google Scholar]
  14. Y. Lin, X. Jiang and W. Zhang, An open-loop Stackelberg strategy for the linear quadratic mean-field stochastic differential game. IEEE Trans. Automat. Contr. 64 (2019) 97–110. [Google Scholar]
  15. B. Wang and J. Zhang, Hierarchical mean field games for multiagent systems with tracking-type costs: distributed ɛ-Stackelberg equilibria. IEEE Trans. Automat. Contr. 59 (2017) 2241–2247. [Google Scholar]
  16. J. Moon and T. Basar, Linear quadratic mean field Stackelberg differential games. Automatica 97 (2018) 200–213. [Google Scholar]
  17. B. Øksendal, L. Sandal and J. Ubøe, Stochastic Stackelberg equilibria with applications to time-dependent newsvendor models. J. Econ. Dyn. Control 37 (2013) 1284–1299. [Google Scholar]
  18. J. Shi, G. Wang and J. Xiong, Leader-follower stochastic differential game with asymmetric information and application. Automatica 63 (2016) 60–73. [Google Scholar]
  19. A. Bensoussan, S. Chen, A. Chutani and S.P. Sethi, Feedback Stackelberg-Nash equilibria in mixed leadership games with an application to cooperative advertising. SIAM J. Control Optim. 57 (2019) 3413–3444. [Google Scholar]
  20. K. Han, X. Rong, Y. Shen and H. Zhao, Continuous-time stochastic mutual fund management game between active and passive funds. Quant. Finance 21 (2021) 1647–1667. [Google Scholar]
  21. D. Hernandez-Hernández and J.H. Ricalde-Guerrero, Zero-sum stochastic games with random rules of priority, discrete linear-quadratic model. Dyn. Games Appl. 12 (2022) 1293–1311. [Google Scholar]
  22. Y.-H. Ni, L. Liu and X. Zhang, Deterministic dynamic Stackelberg games: time-consistent open-loop solution. Automatica J. IFAC 148 (2023) 110757. [Google Scholar]
  23. L. Chen and Y. Shen, Stochastic Stackelberg differential reinsurance games under time-inconsistent mean-variance framework. Insur. Math. Econ. 88 (2019) 120–137. [Google Scholar]
  24. S. Maharjan, Q. Zhu, Y. Zhang, S. Gjessing and T. Basar, Dependable demand response management in the smart grid: a Stackelberg game approach. IEEE Trans. Smart Grid. 4 (2013) 120–132. [Google Scholar]
  25. S.J. Rubio, On coincidence of feedback Nash equilibria and Stackelberg equilibria in economic applications of differential games. J. Optim. Theory Applic. 128 (2006) 203–221. [Google Scholar]
  26. J. Yong and X.Y. Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations. Springer-Verlag, New York (1999). [Google Scholar]
  27. A. Bensoussan, S. Chen and S.P. Sethi, The maximum principle for global solutions of stochastic Stackelberg differential games. SIAM J. Control Optim. 53 (2015) 1956–1981. [Google Scholar]
  28. Z. Yu, On forward–backward stochastic differential equations in a domination-monotonicity framework. Appl. Math. Optim. 85 (2022) 46. [Google Scholar]
  29. J. Yong, A deterministic linear quadratic time-inconsistent optimal control problem. Math. Control Relat. Fields 1 (2011) 83–118. [Google Scholar]
  30. T. Li and S.P. Sethi, A review of dynamic Stackelberg game models. Discrete Contin. Dyn. Syst. Ser. B 22 (2017) 125–159. [Google Scholar]
  31. S. Peng and Z. Wu, Fully coupled forward-backward stochastic differential equations and applications to optimal control. SIAM J. Control Optim. 37 (1999) 825–843. [CrossRef] [MathSciNet] [Google Scholar]

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