Communications in Mathematical Sciences

Volume 13 (2015)

Number 8

Central schemes for mean field games

Pages: 2177 – 2194

DOI: http://dx.doi.org/10.4310/CMS.2015.v13.n8.a9

Authors

Bojan Popov (Department of Mathematics, Texas A&M University, College Station, Tx., U.S.A.)

Vladimir Tomov (Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, California, U.S.A.)

Abstract

Mean field type models have been recently introduced and analyzed by Lasry and Lions. They describe a limiting behavior of stochastic differential games as the number of players tends to infinity. Numerical methods for the approximation of such models have been developed by Achdou, Camilli, Capuzzo-Dolcetta, Gueant, and others. Efficient algorithms for such problems require special efforts and so far all methods introduced have been first order accurate. In this manuscript we design a second order accurate numerical method for time dependent Mean Field Games. The discretization is based on central schemes which are widely used in hyperbolic conservation laws.

Keywords

mean field games, central schemes

2010 Mathematics Subject Classification

65H10, 65M06, 65M12

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Published 3 September 2015