Linear-quadratic-gaussian mean-field-game with partial observation and common noise

Alain Bensoussan, Xinwei Feng, Jianhui Huang

Research output: Journal article publicationJournal articleAcademic researchpeer-review


This paper considers a class of linear-quadratic-Gaussian (LQG) mean-field games (MFGs) with partial observation structure for individual agents. Unlike other literature, there are some special features in our formu-lation. First, the individual state is driven by some common-noise due to the external factor and the state-average thus becomes a random process instead of a deterministic quantity. Second, the sensor function of individual observation depends on state-average thus the agents are coupled in triple manner: not only in their states and cost functionals, but also through their observation mechanism. The decentralized strategies for individual agents are derived by the Kalman filtering and separation principle. The consistency condition is obtained which is equivalent to the wellposedness of some forward-backward stochastic differential equation (FBSDE) driven by common noise. Finally, the related ɛ-Nash equilibrium property is verified.

Original languageEnglish
Pages (from-to)23-46
Number of pages24
JournalMathematical Control and Related Fields
Issue number1
Publication statusPublished - Mar 2021


  • Consistency condition
  • Forward-backward stochastic differential equation
  • Kalman filtering
  • Mean-field games
  • Partial observation
  • ɛ-Nash equilibrium

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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