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A-priori estimates for stationary mean-field games
New numerical methods for mean field games with quadratic costs
1. | UFR de Math, Universit, 175, rue du Chevaleret, 75013 Paris, France |
References:
[1] |
Y. Achdou, F. Camilli and I. Capuzzo-Dolcetta, Mean field games: Numerical methods for the planning problem,, SIAM J. Control Opt., 50 (2012), 77.
doi: 10.1137/100790069. |
[2] |
Y. Achdou and I. Capuzzo-Dolcetta, Mean field games: Numerical methods,, SIAM Journal on Numerical Analysis, 48 (2010), 1136.
doi: 10.1137/090758477. |
[3] |
P. Cardaliaguet, Notes on mean field games,, from P.-L. Lions' lectures at Collège de France, (2010). Google Scholar |
[4] |
M. G. Crandall and P.-L. Lions, Two approximations of solutions of Hamilton-Jacobi equations,, Mathematics of Computation, 43 (1984), 1.
doi: 10.1090/S0025-5718-1984-0744921-8. |
[5] |
L. C. Evans, "Partial Differential Equations,", Graduate Studies in Mathematics, (2010).
|
[6] |
D. A. Gomes, J. Mohr and R. R. Souza, Discrete time, finite state space mean field games,, Journal de Mathématiques Pures et Appliquées (9), 93 (2010), 308.
|
[7] |
O. Guéant, Mean field games equations with quadratic hamiltonian: A specifc approach,, to appear in Mathematical Models and Methods in Applied Sciences (M3AS)., (). Google Scholar |
[8] |
O. Guéant, Mean field games with quadratic hamiltonian: A constructive scheme,, to appear in the Annals of ISDG., (). Google Scholar |
[9] |
O. Guéant, "Mean Field Games and Applications to Economics,", Ph.D thesis, (2009). Google Scholar |
[10] |
O. Guéant, A reference case for mean field games models,, Journal de Mathématiques Pures et Appliquées (9), 92 (2009), 276.
|
[11] |
O. Guéant, J.-M. Lasry and P.-L. Lions, Mean field games and applications,, in, 2003 (2011), 205.
|
[12] |
A. Lachapelle, J. Salomon and G. Turinici, Computation of mean field equilibria in economics,, Mathematical Models and Methods in Applied Sciences, 20 (2010), 567.
doi: 10.1142/S0218202510004349. |
[13] |
J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. I. Le cas stationnaire,, C. R. Acad. Sci. Paris, 343 (2006), 619.
doi: 10.1016/j.crma.2006.09.019. |
[14] |
J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. II. Horizon fini et contrôle optimal,, C. R. Acad. Sci. Paris, 343 (2006), 679.
doi: 10.1016/j.crma.2006.09.018. |
[15] |
J.-M. Lasry and P.-L. Lions, Mean field games,, Japanese Journal of Mathematics, 2 (2007), 229.
|
[16] |
P.-L. Lions, Théorie des jeux à champs moyens, Cours au Collège de France., Available from: \url{http://www.college-de-france.fr/default/EN/all/equ_der/audio_video.jsp}., (). Google Scholar |
show all references
References:
[1] |
Y. Achdou, F. Camilli and I. Capuzzo-Dolcetta, Mean field games: Numerical methods for the planning problem,, SIAM J. Control Opt., 50 (2012), 77.
doi: 10.1137/100790069. |
[2] |
Y. Achdou and I. Capuzzo-Dolcetta, Mean field games: Numerical methods,, SIAM Journal on Numerical Analysis, 48 (2010), 1136.
doi: 10.1137/090758477. |
[3] |
P. Cardaliaguet, Notes on mean field games,, from P.-L. Lions' lectures at Collège de France, (2010). Google Scholar |
[4] |
M. G. Crandall and P.-L. Lions, Two approximations of solutions of Hamilton-Jacobi equations,, Mathematics of Computation, 43 (1984), 1.
doi: 10.1090/S0025-5718-1984-0744921-8. |
[5] |
L. C. Evans, "Partial Differential Equations,", Graduate Studies in Mathematics, (2010).
|
[6] |
D. A. Gomes, J. Mohr and R. R. Souza, Discrete time, finite state space mean field games,, Journal de Mathématiques Pures et Appliquées (9), 93 (2010), 308.
|
[7] |
O. Guéant, Mean field games equations with quadratic hamiltonian: A specifc approach,, to appear in Mathematical Models and Methods in Applied Sciences (M3AS)., (). Google Scholar |
[8] |
O. Guéant, Mean field games with quadratic hamiltonian: A constructive scheme,, to appear in the Annals of ISDG., (). Google Scholar |
[9] |
O. Guéant, "Mean Field Games and Applications to Economics,", Ph.D thesis, (2009). Google Scholar |
[10] |
O. Guéant, A reference case for mean field games models,, Journal de Mathématiques Pures et Appliquées (9), 92 (2009), 276.
|
[11] |
O. Guéant, J.-M. Lasry and P.-L. Lions, Mean field games and applications,, in, 2003 (2011), 205.
|
[12] |
A. Lachapelle, J. Salomon and G. Turinici, Computation of mean field equilibria in economics,, Mathematical Models and Methods in Applied Sciences, 20 (2010), 567.
doi: 10.1142/S0218202510004349. |
[13] |
J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. I. Le cas stationnaire,, C. R. Acad. Sci. Paris, 343 (2006), 619.
doi: 10.1016/j.crma.2006.09.019. |
[14] |
J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. II. Horizon fini et contrôle optimal,, C. R. Acad. Sci. Paris, 343 (2006), 679.
doi: 10.1016/j.crma.2006.09.018. |
[15] |
J.-M. Lasry and P.-L. Lions, Mean field games,, Japanese Journal of Mathematics, 2 (2007), 229.
|
[16] |
P.-L. Lions, Théorie des jeux à champs moyens, Cours au Collège de France., Available from: \url{http://www.college-de-france.fr/default/EN/all/equ_der/audio_video.jsp}., (). Google Scholar |
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