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A-priori estimates for stationary mean-field games
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A semi-discrete approximation for a first order mean field game problem
Long time average of mean field games
| 1. | Ceremade, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16, France, France |
| 2. | 56 Rue d'Assas, 75006 Paris, France |
| 3. | Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scienti ca 1, 00133 Roma, Italy |
References:
| [1] |
Y. Achdou and I. Capuzzo-Dolcetta, Mean field games: Numerical methods, SIAM J. Numer. Anal., 48 (2010), 1136-1162.
doi: 10.1137/090758477. |
| [2] |
Y. Achdou, F. Camilli and I. Capuzzo-Dolcetta, Mean field games: Numerical methods for the planning problem, SIAM J. Control Opt., 50 (2012), 77-109.
doi: 10.1137/100790069. |
| [3] |
M. Arisawa and P.-L. Lions, On ergodic stochastic control, Comm. Partial Differential Equations, 23 (1998), 2187-2217.
doi: 10.1080/03605309808821413. |
| [4] |
G. Barles and P. E. Souganidis, Space-time periodic solutions and long-time behavior of solutions to quasi-linear parabolic equations, SIAM J. Math. Anal., 32 (2001), 1311-1323.
doi: 10.1137/S0036141000369344. |
| [5] |
L. C. Evans, The perturbed test function method for viscosity solutions of nonlinear PDE, Proc. Roy. Soc. Edinburgh Sect. A, 111 (1989), 359-375.
doi: 10.1017/S0308210500018631. |
| [6] |
D. A. Gomes, J. Mohr and R. Souza, Discrete time, finite state space mean field games, J. Math. Pures Appl. (9), 93 (2010), 308-328. |
| [7] |
D. A. Gomes, G. E. Pires and H. Sanchez-Morgado, A-priori estimates for stationary mean-field games, preprint. |
| [8] |
D. A. Gomes and H. Sanchez-Morgado, A stochastic Evans-Aronsson problem, preprint. |
| [9] |
O. Guéant, Mean field games with quadratic hamiltonian: A constructive scheme, preprint. |
| [10] |
O. A. Ladyženskaja, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type," Translations of Mathematical Monographs, Vol. 23, American Mathematical Society, Providence R.I., 1967. |
| [11] |
J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. I. Le cas stationnaire, C. R. Math. Acad. Sci. Paris, 343 (2006), 619-625.
doi: 10.1016/j.crma.2006.09.019. |
| [12] |
J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. II. Horizon fini et contrôle optimal, C. R. Math. Acad. Sci. Paris, 343 (2006), 679-684.
doi: 10.1016/j.crma.2006.09.018. |
| [13] |
J.-M. Lasry and P.-L. Lions, Mean field games, Jpn. J. Math., 2 (2007), 229-260. |
| [14] |
J.-M. Lasry, P.-L. Lions and O. Guéant, Application of mean field games to growth theory, preprint, 2008. |
| [15] |
J.-M. Lasry and P.-L. Lions, Cours au Collège de France. Available from: http://www.college-de-france.fr. |
| [16] |
A. Porretta, Existence results for nonlinear parabolic equations via strong convergence of truncations, Ann. Mat. Pura Appl. (4), 177 (1999), 143-172.
doi: 10.1007/BF02505907. |
show all references
References:
| [1] |
Y. Achdou and I. Capuzzo-Dolcetta, Mean field games: Numerical methods, SIAM J. Numer. Anal., 48 (2010), 1136-1162.
doi: 10.1137/090758477. |
| [2] |
Y. Achdou, F. Camilli and I. Capuzzo-Dolcetta, Mean field games: Numerical methods for the planning problem, SIAM J. Control Opt., 50 (2012), 77-109.
doi: 10.1137/100790069. |
| [3] |
M. Arisawa and P.-L. Lions, On ergodic stochastic control, Comm. Partial Differential Equations, 23 (1998), 2187-2217.
doi: 10.1080/03605309808821413. |
| [4] |
G. Barles and P. E. Souganidis, Space-time periodic solutions and long-time behavior of solutions to quasi-linear parabolic equations, SIAM J. Math. Anal., 32 (2001), 1311-1323.
doi: 10.1137/S0036141000369344. |
| [5] |
L. C. Evans, The perturbed test function method for viscosity solutions of nonlinear PDE, Proc. Roy. Soc. Edinburgh Sect. A, 111 (1989), 359-375.
doi: 10.1017/S0308210500018631. |
| [6] |
D. A. Gomes, J. Mohr and R. Souza, Discrete time, finite state space mean field games, J. Math. Pures Appl. (9), 93 (2010), 308-328. |
| [7] |
D. A. Gomes, G. E. Pires and H. Sanchez-Morgado, A-priori estimates for stationary mean-field games, preprint. |
| [8] |
D. A. Gomes and H. Sanchez-Morgado, A stochastic Evans-Aronsson problem, preprint. |
| [9] |
O. Guéant, Mean field games with quadratic hamiltonian: A constructive scheme, preprint. |
| [10] |
O. A. Ladyženskaja, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type," Translations of Mathematical Monographs, Vol. 23, American Mathematical Society, Providence R.I., 1967. |
| [11] |
J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. I. Le cas stationnaire, C. R. Math. Acad. Sci. Paris, 343 (2006), 619-625.
doi: 10.1016/j.crma.2006.09.019. |
| [12] |
J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. II. Horizon fini et contrôle optimal, C. R. Math. Acad. Sci. Paris, 343 (2006), 679-684.
doi: 10.1016/j.crma.2006.09.018. |
| [13] |
J.-M. Lasry and P.-L. Lions, Mean field games, Jpn. J. Math., 2 (2007), 229-260. |
| [14] |
J.-M. Lasry, P.-L. Lions and O. Guéant, Application of mean field games to growth theory, preprint, 2008. |
| [15] |
J.-M. Lasry and P.-L. Lions, Cours au Collège de France. Available from: http://www.college-de-france.fr. |
| [16] |
A. Porretta, Existence results for nonlinear parabolic equations via strong convergence of truncations, Ann. Mat. Pura Appl. (4), 177 (1999), 143-172.
doi: 10.1007/BF02505907. |
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