Steering the Distribution of Agents in Mean-Field Games System

Yongxin Chen, Tryphon T. Georgiou, Michele Pavon

Research output: Contribution to journalArticlepeer-review


The purpose of this work is to pose and solve the problem to guide a collection of weakly interacting dynamical systems (agents, particles, etc.) to a specified terminal distribution. This is formulated as a mean-field game problem, and is discussed in both non-cooperative games and cooperative games settings. In the non-cooperative games setting, a terminal cost is used to accomplish the task; we establish that the map between terminal costs and terminal probability distributions is onto. In the cooperative games setting, the goal is to find a common optimal control that would drive the distribution of the agents to a targeted one. We focus on the cases when the underlying dynamics is linear and the running cost is quadratic. Our approach relies on and extends the theory of optimal mass transport and its generalizations.

Original languageEnglish (US)
Pages (from-to)332-357
Number of pages26
JournalJournal of Optimization Theory and Applications
Issue number1
StatePublished - Oct 1 2018


  • Linear stochastic systems
  • McKean–Vlasov dynamics
  • Mean-field games
  • Optimal control
  • Weakly interacting particle system

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Control and Optimization
  • Applied Mathematics


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