Discrete methods for fully nonlinear elliptic equations
SIAM Journal on Numerical Analysis
Large-scale games in large-scale systems
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
Mean Field Games: Numerical Methods for the Planning Problem
SIAM Journal on Control and Optimization
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Mean field type models describing the limiting behavior, as the number of players tends to $+\infty$, 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. 619-625; C. R. Math. Acad. Sci. Paris, 343 (2006), pp. 679-684; Jpn. J. Math., 2 (2007), pp. 229-260]. Numerical methods for the approximation 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.