Mixed Linear Quadratic Stochastic Differential Leader-Follower Game with Input Constraint

Tinghan Xie, Xinwei Feng, Jianhui Huang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

7 Citations (Scopus)


This paper investigates a mixed leader-follower differential games problem, where the model involves two players with the same hierarchy in decision making and each player has two controls which act as a leader and a follower, respectively. Specifically, we solve a follower problem with unconstrained controls and obtain the corresponding Nash equilibrium. Then a leader problem with constrained controls is tackled and a pair of optimal constrained controls are presented by a projection mapping. Furthermore, the control weights are allowed to be singular. In this case, we first investigate the uniform convexity of the cost functional whose corresponding states are fully-coupled forward-backward stochastic differential equation. After that, the minimizing sequence of solutions with non-degenerate control weights are constructed to study the weak convergence of the corresponding cost functionals. Finally, two examples are addressed for non-singular and singular cases, respectively.

Original languageEnglish
Pages (from-to)215-251
Number of pages37
JournalApplied Mathematics and Optimization
Issue number1
Early online date15 Apr 2021
Publication statusPublished - Dec 2021


  • Forward-backward stochastic differential equation
  • Input constraint
  • Mixed leader-follower problem
  • Singular control weight
  • Stochastic differential game

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


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