Mean-Field Linear-Quadratic-Gaussian (LQG) Games for Stochastic Integral Systems

Jianhui Huang, Xun Li, Tianxiao Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

13 Citations (Scopus)


In this technical note, we formulate and investigate a class of mean-field linear-quadratic-Gaussian (LQG) games for stochastic integral systems. Unlike other literature on mean-field games where the individual states follow the controlled stochastic differential equations (SDEs), the individual states in our large-population system are characterized by a class of stochastic Volterra-type integral equations. We obtain the Nash certainty equivalence (NCE) equation and hence derive the set of associated decentralized strategies. The ϵ-Nash equilibrium properties are also verified. Due to the intrinsic integral structure, the techniques and estimates applied here are significantly different from those existing results in mean-field LQG games for stochastic differential systems. For example, some Fredholm equation in the mean-field setup is introduced for the first time. As for applications, two types of stochastic delayed systems are formulated as the special cases of our stochastic integral system, and relevant mean-field LQG games are discussed.
Original languageEnglish
Article number7349148
Pages (from-to)2670-2675
Number of pages6
JournalIEEE Transactions on Automatic Control
Issue number9
Publication statusPublished - 1 Sept 2016


  • Controlled stochastic delay system
  • Fredholm equation
  • mean field LQG games
  • stochastic Volterra equation
  • ϵ-Nash equilibrium

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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