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Mean Field Games

Encyclopedia of Systems and Control

Definition

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.

Introduction

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...

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Author information

Authors and Affiliations

  1. McGill University, Montreal, QC, Canada

    Peter E Caines

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  1. Peter E Caines
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Correspondence to Peter E Caines .

Editor information

Editors and Affiliations

  1. Electrical and Computer Engineering, Boston University, Boston, Massachusetts, USA

    John Baillieul

  2. Automation and Control Solutions, Honeywell, Golden Valley, Minnesota, USA

    Tariq Samad

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© 2013 Springer-Verlag London

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Caines, P.E. (2013). Mean Field Games. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_30-1

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_30-1

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  • Online ISBN: 978-1-4471-5102-9

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Chapter history

  1. Latest

    Mean Field Games
    Published:
    24 September 2019

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_30-2

  2. Original

    Mean Field Games
    Published:
    28 February 2014

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_30-1

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