Linear-quadratic-Gaussian mixed mean-field games with heterogeneous input constraints

Ying Hu, Jianhui Huang, Tianyang Nie

Research output: Journal article publicationJournal articleAcademic researchpeer-review

29 Citations (Scopus)


We consider a class of linear-quadratic-Gaussian mean-field games having a major agent and numerous heterogeneous minor agents in the presence of mean-field interactions. The individual admissible controls are constrained in closed convex subsets Γk of Rm. The decentralized strategies of individual agents and the consistency condition system are represented in a unified manner through a class of mean-field forward-backward stochastic differential equations involving projection operators on Γk. The well-posedness of the consistency system is established in both the local and global cases through the contraction mapping and discounting methods, respectively. A related ε-Nash-equilibrium property is also verified.

Original languageEnglish
Pages (from-to)2835-2877
Number of pages43
JournalSIAM Journal on Control and Optimization
Issue number4
Publication statusPublished - 1 Aug 2018


  • Forward-backward stochastic differential equation
  • Input constraint
  • Linear-quadratic mixed mean-field games
  • Projection operator
  • Ε-Nash equilibrium

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


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