Mean field games: numerical methods, SIAM J. Numer. Anal, vol.48, issue.3, pp.1136-1162, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00392074
Convergence of a finite difference scheme to weak solutions of the system of partial differential equations arising in mean field games, SIAM J. Numer. Anal, vol.54, issue.1, pp.161-186, 2016. ,
Mean field games with congestion, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol.35, issue.2, pp.443-480, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01544509
Invisible control of self-organizing agents leaving unknown environments, SIAM J. Appl. Math, vol.76, issue.4, pp.1683-1710, 2016. ,
Transport equation and Cauchy problem for non-smooth vector fields, Calculus of variations and nonlinear partial differential equations, vol.1927, pp.1-41, 2008. ,
Functions of bounded variation and free discontinuity problems, Oxford Mathematical Monographs, 2000. ,
Gradient flows in metric spaces and in the space of probability measures, Lectures in Mathematics ETH Zürich. Birkhäuser Verlag, 2005. ,
Set-valued analysis. Modern Birkhäuser Classics, 2009. ,
Advances in theory, models, and applications, Active particles, vol.1, pp.141-171, 2017. ,
On the interpretation of the Master Equation, Stochastic Process. Appl, vol.127, issue.7, pp.2093-2137, 2017. ,
, Topologie Générale. Chapitres 5à 10.Éléments de Mathématique, 2007.
On a mean field game optimal control approach modeling fast exit scenarios in human crowds, 52nd IEEE Conference on Decision and Control, 2013. ,
A numerical method for mean field games on networks, ESAIM Math. Model. Numer. Anal, vol.51, issue.1, pp.63-88, 2017. ,
A model problem for mean field games on networks, Discrete Contin. Dyn. Syst, vol.35, issue.9, pp.4173-4192, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01098206
Existence and uniqueness for mean field games with state constraints, PDE models for multi-agent phenomena, vol.28, pp.49-71, 2018. ,
Local regularity of the value function in optimal control, Systems Control Lett, vol.62, issue.9, pp.791-794, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00851753
Semiconcave functions, Hamilton-Jacobi equations, and optimal control, Progress in Nonlinear Differential Equations and their Applications, vol.58, 2004. ,
Long time average of first order mean field games and weak KAM theory, Dyn. Games Appl, vol.3, issue.4, pp.473-488, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00827956
Notes on mean field games (from P.-L. Lions' lectures at Collège de France), 2013. ,
Weak solutions for first order mean field games with local coupling, Analysis and geometry in control theory and its applications, vol.11, pp.111-158, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-00827957
The convergence problem in mean field games with local coupling, Applied Mathematics & Optimization, vol.76, issue.1, pp.177-215, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01384333
The master equation and the convergence problem in mean field games, Annals of Mathematics Studies, vol.201, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-01196045
Long time average of mean field games with a nonlocal coupling, SIAM J. Control Optim, vol.51, issue.5, pp.3558-3591, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00914803
First order mean field games with density constraints: pressure equals price, SIAM J. Control Optim, vol.54, issue.5, pp.2672-2709, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01173947
Optimal transportation with traffic congestion and Wardrop equilibria, SIAM J. Control Optim, vol.47, issue.3, pp.1330-1350, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00361010
A continuous theory of traffic congestion and Wardrop equilibria, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), vol.390, pp.307-308, 2011. ,
A fully discrete semi-Lagrangian scheme for a first order mean field game problem, SIAM J. Numer. Anal, vol.52, issue.1, pp.45-67, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00800507
The master equation for large population equilibriums, Stochastic analysis and applications, vol.100, pp.77-128, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00979789
Time-dependent focusing mean-field games: the sub-critical case, J. Dynam. Differential Equations, vol.31, issue.1, pp.49-79, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-01508506
Pedestrian flows and non-classical shocks, Math. Methods Appl. Sci, vol.28, issue.13, pp.1553-1567, 2005. ,
A destination-preserving model for simulating Wardrop equilibria in traffic flow on networks, Netw. Heterog. Media, vol.10, issue.4, pp.857-876, 2015. ,
Modeling rationality to control self-organization of crowds: an environmental approach, SIAM J. Appl. Math, vol.75, issue.2, pp.605-629, 2015. ,
Shape analysis via oriented distance functions, J. Funct. Anal, vol.123, issue.1, pp.129-201, 1994. ,
Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math, vol.98, issue.3, pp.511-547, 1989. ,
Optimal transportation with boundary costs and summability estimates on the transport density, J. Convex Anal, vol.25, issue.1, pp.135-160, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01370885
First-order, stationary mean-field games with congestion, Nonlinear Anal, vol.173, pp.37-74, 2018. ,
Crowd motion from the granular standpoint, Math. Models Methods Appl. Sci, vol.25, issue.3, pp.463-493, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01358423
Existence for stationary mean-field games with congestion and quadratic Hamiltonians, NoDEA Nonlinear Differential Equations Appl, vol.22, issue.6, pp.1897-1910, 2015. ,
Continuous time finite state mean field games, Appl. Math. Optim, vol.68, issue.1, pp.99-143, 2013. ,
Mean field games models-a brief survey, Dyn. Games Appl, vol.4, issue.2, pp.110-154, 2014. ,
Short-time existence of solutions for mean-field games with congestion, J. Lond. Math. Soc, vol.92, issue.2, pp.778-799, 2015. ,
Fixed point theory, 2003. ,
New numerical methods for mean field games with quadratic costs, Netw. Heterog. Media, vol.7, issue.2, pp.315-336, 2012. ,
Existence and uniqueness result for mean field games with congestion effect on graphs, Appl. Math. Optim, vol.72, issue.2, pp.291-303, 2015. ,
Mean field games and applications, Paris-Princeton Lectures on Mathematical Finance, pp.205-266, 2003. ,
Simulating dynamical features of escape panic, Nature, vol.407, issue.6803, p.487, 2000. ,
The statistics of crowd fluids, Nature, vol.229, issue.5284, pp.381-383, 1971. ,
Individual and mass behaviour in large population stochastic wireless power control problems: centralized and Nash equilibrium solutions, 42nd IEEE Conference on Decision and Control, vol.1, pp.98-103, 2003. ,
Large-population cost-coupled LQG problems with nonuniform agents: individual-mass behavior and decentralized ?-Nash equilibria, IEEE Trans. Automat. Control, vol.52, issue.9, pp.1560-1571, 2007. ,
Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle, Commun. Inf. Syst, vol.6, issue.3, pp.221-251, 2006. ,
A continuum theory for the flow of pedestrians, Transportation Research Part B: Methodological, vol.36, issue.6, pp.507-535, 2002. ,
The flow of human crowds, Annu. Rev. Fluid Mech, vol.35, pp.169-182, 2003. ,
A generalization of Brouwer's fixed point theorem, Duke Math. J, vol.8, pp.457-459, 1941. ,
On the rate of convergence for the mean-field approximation of controlled diffusions with large number of players, Dyn. Games Appl, vol.4, issue.2, pp.208-230, 2014. ,
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. ,
URL : https://hal.archives-ouvertes.fr/hal-00554898
Jeuxà champ moyen. I. Le cas stationnaire, C. R. Math. Acad. Sci, vol.343, issue.9, pp.619-625, 2006. ,
Jeuxà champ moyen. II. Horizon fini et contrôle optimal, C. R. Math. Acad. Sci, vol.343, issue.10, pp.679-684, 2006. ,
Mean field games, Jpn. J. Math, vol.2, issue.1, pp.229-260, 2007. ,
URL : https://hal.archives-ouvertes.fr/hal-00667356
A macroscopic crowd motion model of gradient flow type, Math. Models Methods Appl. Sci, vol.20, issue.10, pp.1787-1821, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00418511
Minimal-time mean field games, Math. Models Methods Appl. Sci, vol.29, issue.8, pp.1413-1464, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-01768363
A variational approach to second order mean field games with density constraints: the stationary case, J. Math. Pures Appl, vol.104, issue.9, pp.1135-1159, 2015. ,
Time-evolving measures and macroscopic modeling of pedestrian flow, Arch. Ration. Mech. Anal, vol.199, issue.3, pp.707-738, 2011. ,
Global-in-time regularity via duality for congestion-penalized mean field games, Stochastics, vol.89, issue.6-7, pp.923-942, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01295289
Optimal transport for applied mathematicians, Calculus of variations, PDEs, and modeling, vol.87, 2015. ,
Optimal transport, vol.338 ,
URL : https://hal.archives-ouvertes.fr/hal-00923320
Old and new, 2009. ,
Some theoretical aspects of road traffic research, Proc. Inst. Civ. Eng, vol.1, issue.3, pp.325-362 ,
E-mail address: samer.dweik@math.u-psud.fr ,
E-mail address: guilherme.mazanti@math.u-psud.fr ,