-
1
-
-
77549085949
-
Discrete time, finite state space mean field games
-
Gomes, D.A., Mohr, J., Souza, R.R., Discrete time, finite state space mean field games. J. Math. Pures Appl. 93:3 (2010), 308–328.
-
(2010)
J. Math. Pures Appl.
, vol.93
, Issue.3
, pp. 308-328
-
-
Gomes, D.A.1
Mohr, J.2
Souza, R.R.3
-
2
-
-
85011536691
-
Learning in mean field games: the fictitious play
-
Cardaliaguet, P., Hadikhanloo, S., Learning in mean field games: the fictitious play. ESAIM Control Optim. Calc. Var. 23:2 (2017), 569–591.
-
(2017)
ESAIM Control Optim. Calc. Var.
, vol.23
, Issue.2
, pp. 569-591
-
-
Cardaliaguet, P.1
Hadikhanloo, S.2
-
3
-
-
85061629081
-
Learning in anonymous nonatomic games with applications to first-order mean field games
-
arXiv preprint
-
Hadikhanloo, S., Learning in anonymous nonatomic games with applications to first-order mean field games. arXiv preprint arXiv:1704.00378.
-
-
-
Hadikhanloo, S.1
-
4
-
-
33750627999
-
Jeux à champ moyen. I—Le cas stationnaire
-
Lasry, J.-M., Lions, P.-L., Jeux à champ moyen. I—Le cas stationnaire. C. R. Math. 343:9 (2006), 619–625.
-
(2006)
C. R. Math.
, vol.343
, Issue.9
, pp. 619-625
-
-
Lasry, J.-M.1
Lions, P.-L.2
-
5
-
-
33751077273
-
Jeux à champ moyen. II—Horizon fini et contrôle optimal
-
Lasry, J.-M., Lions, P.-L., Jeux à champ moyen. II—Horizon fini et contrôle optimal. C. R. Math. 343:10 (2006), 679–684.
-
(2006)
C. R. Math.
, vol.343
, Issue.10
, pp. 679-684
-
-
Lasry, J.-M.1
Lions, P.-L.2
-
6
-
-
34047127341
-
Mean field games
-
Lasry, J.-M., Lions, P.-L., Mean field games. Jpn. J. Math. 2:1 (2007), 229–260.
-
(2007)
Jpn. J. Math.
, vol.2
, Issue.1
, pp. 229-260
-
-
Lasry, J.-M.1
Lions, P.-L.2
-
7
-
-
39549087376
-
Large population stochastic dynamic games: closed-loop McKean–Vlasov systems and the Nash certainty equivalence principle
-
Huang, M., Malhamé, R.P., Caines, P.E., Large population stochastic dynamic games: closed-loop McKean–Vlasov systems and the Nash certainty equivalence principle. Commun. Inf. Syst. 6:3 (2006), 221–252.
-
(2006)
Commun. Inf. Syst.
, vol.6
, Issue.3
, pp. 221-252
-
-
Huang, M.1
Malhamé, R.P.2
Caines, P.E.3
-
8
-
-
85072069003
-
The master equation and the convergence problem in mean field games
-
arXiv preprint
-
Cardaliaguet, P., Delarue, F., Lasry, J.-M., Lions, P.-L., The master equation and the convergence problem in mean field games. arXiv preprint arXiv:1509.02505.
-
-
-
Cardaliaguet, P.1
Delarue, F.2
Lasry, J.-M.3
Lions, P.-L.4
-
9
-
-
84865537156
-
Cours au Collège de France
-
Lions, P.-L., Cours au Collège de France. www.college-de-france.fr.
-
-
-
Lions, P.-L.1
-
10
-
-
85068762191
-
Notes on Mean Field Games
-
Tech. rep., Technical report
-
Cardaliaguet, P., Notes on Mean Field Games. Tech. rep., Technical report, 2010.
-
(2010)
-
-
Cardaliaguet, P.1
-
11
-
-
77958476920
-
Mean field games and applications
-
Guéant, O., Lasry, J.-M., Lions, P.-L., Mean field games and applications. Paris–Princeton Lectures on Mathematical Finance 2010, vol. 2003, 2011, 205–266.
-
(2011)
Paris–Princeton Lectures on Mathematical Finance 2010
, vol.2003
, pp. 205-266
-
-
Guéant, O.1
Lasry, J.-M.2
Lions, P.-L.3
-
12
-
-
84899464039
-
Mean field games models—a brief survey
-
Gomes, D.A., Saúde, J., Mean field games models—a brief survey. Dyn. Games Appl. 4:2 (2014), 110–154, 10.1007/s13235-013-0099-2.
-
(2014)
Dyn. Games Appl.
, vol.4
, Issue.2
, pp. 110-154
-
-
Gomes, D.A.1
Saúde, J.2
-
13
-
-
85101139683
-
Regularity Theory for Mean-Field Game Systems
-
Springer Cham
-
Gomes, D.A., Pimentel, E.A., Voskanyan, V., Regularity Theory for Mean-Field Game Systems. SpringerBriefs in Mathematics, 2016, Springer, Cham, 10.1007/978-3-319-38934-9.
-
(2016)
SpringerBriefs in Mathematics
-
-
Gomes, D.A.1
Pimentel, E.A.2
Voskanyan, V.3
-
14
-
-
0002672918
-
Iterative solution of games by fictitious play
-
Brown, G.W., Iterative solution of games by fictitious play. Act. Anal. Prod. Allocation 13:1 (1951), 374–376.
-
(1951)
Act. Anal. Prod. Allocation
, vol.13
, Issue.1
, pp. 374-376
-
-
Brown, G.W.1
-
15
-
-
0004247096
-
The Theory of Learning in Games
-
MIT Press
-
Fudenberg, D., Levine, D.K., The Theory of Learning in Games. vol. 2, 1998, MIT Press.
-
(1998)
, vol.2
-
-
Fudenberg, D.1
Levine, D.K.2
-
16
-
-
77956048120
-
Mean field games: numerical methods
-
Achdou, Y., Capuzzo-Dolcetta, I., Mean field games: numerical methods. SIAM J. Numer. Anal. 48:3 (2010), 1136–1162.
-
(2010)
SIAM J. Numer. Anal.
, vol.48
, Issue.3
, pp. 1136-1162
-
-
Achdou, Y.1
Capuzzo-Dolcetta, I.2
-
17
-
-
84890625353
-
Mean field games: convergence of a finite difference method
-
Achdou, Y., Camilli, F., Capuzzo-Dolcetta, I., Mean field games: convergence of a finite difference method. SIAM J. Numer. Anal. 51:5 (2013), 2585–2612.
-
(2013)
SIAM J. Numer. Anal.
, vol.51
, Issue.5
, pp. 2585-2612
-
-
Achdou, Y.1
Camilli, F.2
Capuzzo-Dolcetta, I.3
-
18
-
-
84960841215
-
Convergence of a finite difference scheme to weak solutions of the system of partial differential equations arising in mean field games
-
Achdou, Y., Porretta, A., 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. 54:1 (2016), 161–186, 10.1137/15M1015455.
-
(2016)
SIAM J. Numer. Anal.
, vol.54
, Issue.1
, pp. 161-186
-
-
Achdou, Y.1
Porretta, A.2
-
19
-
-
84897834273
-
A fully discrete semi-Lagrangian scheme for a first order mean field game problem
-
Carlini, E., Silva, F.J., A fully discrete semi-Lagrangian scheme for a first order mean field game problem. SIAM J. Numer. Anal. 52:1 (2014), 45–67.
-
(2014)
SIAM J. Numer. Anal.
, vol.52
, Issue.1
, pp. 45-67
-
-
Carlini, E.1
Silva, F.J.2
-
20
-
-
84926639229
-
A semi-Lagrangian scheme for a degenerate second order mean field game system
-
Carlini, E., Silva, F.J., A semi-Lagrangian scheme for a degenerate second order mean field game system. Discrete Contin. Dyn. Syst. 35:9 (2015), 4269–4292, 10.3934/dcds.2015.35.4269.
-
(2015)
Discrete Contin. Dyn. Syst.
, vol.35
, Issue.9
, pp. 4269-4292
-
-
Carlini, E.1
Silva, F.J.2
-
21
-
-
85053488827
-
On the discretization of some nonlinear Fokker–Planck–Kolmogorov equations and applications
-
Carlini, E., Silva, F.J., On the discretization of some nonlinear Fokker–Planck–Kolmogorov equations and applications. SIAM J. Numer. Anal. 56:4 (2018), 2148–2177, 10.1137/17M1143022.
-
(2018)
SIAM J. Numer. Anal.
, vol.56
, Issue.4
, pp. 2148-2177
-
-
Carlini, E.1
Silva, F.J.2
-
22
-
-
31744443874
-
Gradient Flows: In Metric Spaces and in the Space of Probability Measures
-
Springer Science & Business Media
-
Ambrosio, L., Gigli, N., Savaré, G., Gradient Flows: In Metric Spaces and in the Space of Probability Measures. 2008, Springer Science & Business Media.
-
(2008)
-
-
Ambrosio, L.1
Gigli, N.2
Savaré, G.3
-
23
-
-
2442557820
-
Topics in Optimal Transportation
-
American Mathematical Society Providence, RI
-
Villani, C., Topics in Optimal Transportation. Graduate Studies in Mathematics., vol. 58, 2003, American Mathematical Society, Providence, RI.
-
(2003)
Graduate Studies in Mathematics.
, vol.58
-
-
Villani, C.1
-
24
-
-
85030238377
-
Variational mean field games
-
Model. Simul. Sci. Eng. Technol., Birkhäuser/Springer Cham
-
Benamou, J.-D., Carlier, G., Santambrogio, F., Variational mean field games. Active Particles. Vol. 1. Advances in Theory, Models, and Applications, 2017, Model. Simul. Sci. Eng. Technol., Birkhäuser/Springer, Cham, 141–171.
-
(2017)
Active Particles. Vol. 1. Advances in Theory, Models, and Applications
, pp. 141-171
-
-
Benamou, J.-D.1
Carlier, G.2
Santambrogio, F.3
-
25
-
-
85059103630
-
-
Existence and uniqueness for Mean Field Games with state constraints, preprint.
-
P. Cannarsa, R. Capuani, Existence and uniqueness for Mean Field Games with state constraints, preprint.
-
-
-
Cannarsa, P.1
Capuani, R.2
-
26
-
-
0003448545
-
Partial Differential Equations
-
American Mathematical Society Providence, RI
-
Evans, L.C., Partial Differential Equations. 2010, American Mathematical Society, Providence, RI.
-
(2010)
-
-
Evans, L.C.1
-
27
-
-
79958280406
-
Convex Hamilton–Jacobi equations under superlinear growth conditions on data
-
Da Lio, F., Ley, O., Convex Hamilton–Jacobi equations under superlinear growth conditions on data. Appl. Math. Optim. 63:3 (2011), 309–339, 10.1007/s00245-010-9122-9.
-
(2011)
Appl. Math. Optim.
, vol.63
, Issue.3
, pp. 309-339
-
-
Da Lio, F.1
Ley, O.2
-
28
-
-
0011074435
-
On the Bellman equation for some unbounded control problems
-
Bardi, M., Da Lio, F., On the Bellman equation for some unbounded control problems. NoDEA Nonlinear Differ. Equ. Appl. 4:4 (1997), 491–510, 10.1007/s000300050027.
-
(1997)
NoDEA Nonlinear Differ. Equ. Appl.
, vol.4
, Issue.4
, pp. 491-510
-
-
Bardi, M.1
Da Lio, F.2
-
29
-
-
0003809134
-
Optimal Control and Viscosity Solutions of Hamilton–Jacobi–Bellman Equations
-
Birkhäuser Boston, Inc. Boston, MA with appendices by Maurizio Falcone and Pierpaolo Soravia
-
Bardi, M., Capuzzo-Dolcetta, I., Optimal Control and Viscosity Solutions of Hamilton–Jacobi–Bellman Equations. Systems & Control: Foundations & Applications, 1997, Birkhäuser Boston, Inc., Boston, MA, 10.1007/978-0-8176-4755-1 with appendices by Maurizio Falcone and Pierpaolo Soravia.
-
(1997)
Systems & Control: Foundations & Applications
-
-
Bardi, M.1
Capuzzo-Dolcetta, I.2
-
30
-
-
84974753170
-
Convergence of approximation schemes for fully nonlinear second order equations
-
Barles, G., Souganidis, P.E., Convergence of approximation schemes for fully nonlinear second order equations. Asymptot. Anal. 4:3 (1991), 271–283.
-
(1991)
Asymptot. Anal.
, vol.4
, Issue.3
, pp. 271-283
-
-
Barles, G.1
Souganidis, P.E.2
-
31
-
-
84887524276
-
Long time average of first order mean field games and weak KAM theory
-
Cardaliaguet, P., Long time average of first order mean field games and weak KAM theory. Dyn. Games Appl. 3:4 (2013), 473–488.
-
(2013)
Dyn. Games Appl.
, vol.3
, Issue.4
, pp. 473-488
-
-
Cardaliaguet, P.1
-
32
-
-
0010858699
-
Semiconcave Functions, Hamilton–Jacobi Equations, and Optimal Control
-
Springer Science & Business Media
-
Cannarsa, P., Sinestrari, C., Semiconcave Functions, Hamilton–Jacobi Equations, and Optimal Control. vol. 58, 2004, Springer Science & Business Media.
-
(2004)
, vol.58
-
-
Cannarsa, P.1
Sinestrari, C.2
|