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PDE Models for Multi-Agent Phenomena pp 21–47Cite as

Finite Difference Methods for Mean Field Games Systems

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Part of the book series: Springer INdAM Series ((SINDAMS,volume 28))

Abstract

We discuss convergence results for a class of finite difference schemes approximating Mean Field Games systems either on the torus or a network. We also propose a quasi-Newton method for the computation of discrete solutions, based on a least squares formulation of the problem. Several numerical experiments are carried out including the case with two or more competing populations.

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Author information

Authors and Affiliations

  1. Dip. di Matematica e Fisica, Università degli Studi Roma Tre, Rome, Italy

    Simone Cacace

  2. Dip. di Scienze di Base e Applicate per l’Ingegneria, “Sapienza” Università di Roma, Rome, Italy

    Fabio Camilli

Authors
  1. Simone Cacace
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  2. Fabio Camilli
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Corresponding author

Correspondence to Fabio Camilli .

Editor information

Editors and Affiliations

  1. Ceremade, Université Paris-Dauphine, Paris, France

    Pierre Cardaliaguet

  2. Dept. of Mathematics, Universitá di Roma “Tor Vergata”, Roma, Italy

    Alessio Porretta

  3. Dept. of Mathematics “F. Casorati”, University of Pavia, Pavia, Italy

    Francesco Salvarani

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Cacace, S., Camilli, F. (2018). Finite Difference Methods for Mean Field Games Systems. In: Cardaliaguet, P., Porretta, A., Salvarani, F. (eds) PDE Models for Multi-Agent Phenomena. Springer INdAM Series, vol 28. Springer, Cham. https://doi.org/10.1007/978-3-030-01947-1_2

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