Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Mean Field Games

  • Peter E CainesEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5102-9_30-1


Mean Field Game (MFG) theory studies the existence of Nash equilibria, together with the individual strategies which generate them, in games involving a large number of agents modeled by controlled stochastic dynamical systems. This is achieved by exploiting the relationship between the finite and corresponding infinite limit population problems. The solution of the infinite population problem is given by the fundamental MFG Hamilton-Jacobi-Bellman (HJB) and Fokker-Planck-Kolmogorov (FPK) equations which are linked by the state distribution of a generic agent, otherwise known as the system’s mean field.


Large-population, dynamical, multi-agent, competitive, and cooperative phenomena occur in a wide range of designed and natural settings such as communication, environmental, epidemiological, transportation, and energy systems, and they underlie much economic and financial behavior. Analysis of such systems is intractable using the finite population game theoretic...


Nash Equilibrium Stochastic Differential Equation Finite Population Infinite Population Infinite Time Horizon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.McGill UniversityMontrealCanada