 
Summary: SIAM J. NUMER. ANAL. c 2010 Society for Industrial and Applied Mathematics
Vol. 48, No. 3, pp. 11361162
MEAN FIELD GAMES: NUMERICAL METHODS
YVES ACHDOU AND ITALO CAPUZZODOLCETTA
Abstract. Mean field type models describing the limiting behavior, as the number of players
tends to +, of stochastic differential game problems, have been recently introduced by J.M. Lasry
and P.L. Lions [C. R. Math. Acad. Sci. Paris, 343 (2006), pp. 619625; C. R. Math. Acad. Sci. Paris,
343 (2006), pp. 679684; Jpn. J. Math., 2 (2007), pp. 229260]. Numerical methods for the approx
imation of the stationary and evolutive versions of such models are proposed here. In particular,
existence and uniqueness properties as well as bounds for the solutions of the discrete schemes are
investigated. Numerical experiments are carried out.
Key words. mean field games, finite difference schemes
AMS subject classifications. 65M06, 65M012, 9108, 91A23, 49L25
DOI. 10.1137/090758477
1. Introduction. Mean field type models describing the limiting behavior of
stochastic differential game problems as the number of players tends to + have
recently been introduced by J.M. Lasry and P.L. Lions [11, 12, 13]. In the stationary
setting, a typical model of this kind comprises the following system:
u + H(x, u) + = V [m] in T2
,(1)
