Encyclopedia of Systems and Control

2015 Edition
| Editors: John Baillieul, Tariq Samad

Mean Field Games

  • Peter E. Caines
Reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5058-9_30

Abstract

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.

Keywords

Fokker-Planck-Kolmogorov (FPK) equation Hamilton-Jacobi-Bellman (HJB) equation Nash equilibrium Stochastic dynamical systems 
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Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  • Peter E. Caines
    • 1
  1. 1.McGill UniversityMontrealCanada