Y. Achdou, F. Camilli, and I. Capuzzo-dolcetta, Mean Field Games: Numerical Methods for the Planning Problem, SIAM Journal on Control and Optimization, vol.50, issue.1, pp.77-109, 2012.
DOI : 10.1137/100790069

URL : https://hal.archives-ouvertes.fr/hal-00465404

Y. Achdou, F. Camilli, and I. C. Dolcetta, Mean Field Games: Convergence of a Finite Difference Method, SIAM Journal on Numerical Analysis, vol.51, issue.5, 2012.
DOI : 10.1137/120882421

URL : https://hal.archives-ouvertes.fr/hal-01456506

Y. Achdou, F. Camilli, and L. Corrias, On numerical approximations of the Hamillton-Jacobitransport system arysing in high frequency, 2011.

Y. Achdou and I. Capuzzo-dolcetta, Mean Field Games: Numerical Methods, SIAM Journal on Numerical Analysis, vol.48, issue.3, pp.1136-1162, 2010.
DOI : 10.1137/090758477

URL : https://hal.archives-ouvertes.fr/hal-00392074

L. Ambrosio, N. Gigli, and G. Savaré, Gradient flows in metric spaces and in the space of probability measures, Lectures in Mathematics ETH Zürich. Birkhäuser Verlag, 2008.

J. Aubin and H. Frankowska, Set-valued analysis, volume 2 of Systems & Control: Foundations & Applications, Birkhäuser Boston Inc, 1990.

R. Aumann, Markets with a Continuum of Traders, Econometrica, vol.32, issue.1/2, 1964.
DOI : 10.2307/1913732

M. Bardi and I. Capuzzo-dolcetta, Optimal control and viscosity solutions of Hamilton- Jacobi-Bellman equations. Systems & Control: Foundations & Applications, With appendices by Maurizio Falcone and Pierpaolo Soravia, 1997.

G. Barles and P. E. Souganidis, Convergence of approximation schemes for fully nonlinear second order equations, 29th IEEE Conference on Decision and Control, pp.271-283, 1991.
DOI : 10.1109/CDC.1990.204046

F. Camilli and F. J. Silva, A semi-discrete in time approximation for a first order-finite mean field game problem, Network and Heterogeneous Media, pp.7-2263, 2012.

P. Cannarsa and C. Sinestrari, Semiconcave functions, Hamilton-Jacobi equations, and optimal control, Progress in Nonlinear Differential Equations and their Applications, 2004.

P. Cardaliaguet, Notes on mean field games: from P.-L. Lions' lectures atColì ege de France. Lecture Notes given at Tor Vergata, 2010.

E. Carlini, M. Falcone, and R. Ferretti, Convergence of a large time-step scheme for mean curvature motion. Interfaces Free Bound, pp.409-441, 2010.

P. G. Ciarlet and J. Lions, Handbook of numerical analysis Handbook of Numerical Analysis, II. North-Holland Finite element methods, 1991.

M. Falcone and R. Ferretti, Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations, MOS-SIAM Series on Optimization
DOI : 10.1137/1.9781611973051

URL : https://hal.archives-ouvertes.fr/hal-00916055

L. Gosse and F. James, Convergence results for an inhomogeneous system arising in various high frequency approximations, Numerische Mathematik, vol.90, issue.4, pp.721-753, 2002.
DOI : 10.1007/s002110100309

URL : https://hal.archives-ouvertes.fr/hal-00079237

O. Guéant, MEAN FIELD GAMES EQUATIONS WITH QUADRATIC HAMILTONIAN: A SPECIFIC APPROACH, Mathematical Models and Methods in Applied Sciences, vol.22, issue.09, 2012.
DOI : 10.1142/S0218202512500224

O. Guéant, J. , and P. Lions, Mean Field Games and Applications, Paris- Princeton Lectures on Mathematical Finance 2010, pp.205-266, 2003.
DOI : 10.1007/978-3-642-14660-2_3

A. Lachapelle and M. Wolfram, On a mean field game approach modeling congestion and aversion in pedestrian crowds, Transportation Research Part B: Methodological, vol.45, issue.10, pp.1572-1589, 2011.
DOI : 10.1016/j.trb.2011.07.011

URL : https://hal.archives-ouvertes.fr/hal-00554898

J. Lasry and P. Lions, Jeux ?? champ moyen. I ??? Le cas stationnaire, Comptes Rendus Mathematique, vol.343, issue.9, pp.619-625, 2006.
DOI : 10.1016/j.crma.2006.09.019

J. Lasry and P. Lions, JeuxàJeuxà champ moyen. II. Horizon fini et contrôle optimal, C. R. Math. Acad. Sci. Paris, issue.10, pp.343679-684, 2006.

J. Lasry and P. Lions, Mean field games, Japanese Journal of Mathematics, vol.4, issue.1, pp.229-260, 2007.
DOI : 10.1007/s11537-007-0657-8

URL : https://hal.archives-ouvertes.fr/hal-00667356

C. Lin and E. Tadmor, $L^1$-Stability and error estimates for approximate Hamilton-Jacobi solutions, Numerische Mathematik, vol.87, issue.4, pp.701-735, 2001.
DOI : 10.1007/PL00005430

P. Lions, Cours auColì ege de France. www.college-de-france.fr, 2007.

S. Osher and R. Fedkiw, Level set methods and dynamic implicit surfaces, Applied Mathematical Sciences, vol.153, 2003.

B. Piccoli and A. Tosin, Time-Evolving Measures and Macroscopic Modeling of Pedestrian Flow, Archive for Rational Mechanics and Analysis, vol.4, issue.2, pp.707-738, 2011.
DOI : 10.1007/s00205-010-0366-y

F. Poupaud and M. Rascle, Measure solutions to the linear multi-dimensional transport equation with non-smooth coefficients, Communications in Partial Differential Equations, vol.1042, issue.1-2, pp.337-358, 1997.
DOI : 10.1070/SM1967v002n02ABEH002340

J. A. Sethian, Level set methods and fast marching methods, volume 3 of Cambridge Monographs on Applied and Computational Mathematics Evolving interfaces in computational geometry, fluid mechanics , computer vision, and materials science, 1999.

A. Tosin and P. Frasca, Existence and approximation of probability measure solutions to models of collective behaviors, Netw. Heterog. Media, vol.6, issue.3, pp.561-596, 2011.