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A-priori estimates for stationary mean-field games
1. | Departamento de Matemática and CAMGSD, IST Avenida Rovisco Pais, Lisboa, Portugal, Portugal |
2. | Instituto de Matem, Universidad Nacional Aut, M, Mexico |
References:
[1] |
Y. Achdou and I. Capuzzo-Dolcetta, Mean field games: Numerical methods,, SIAM J. Numer. Anal., 48 (2010), 1136.
doi: 10.1137/090758477. |
[2] |
Julien Salomon, Aimée Lachapelle and Gabriel Turinici, Computation of mean field equilibria in economics,, Math. Models Methods Appl. Sci., 20 (2010), 567.
doi: 10.1142/S0218202510004349. |
[3] |
F. Camilli, Y. Achdou and I. Capuzzo-Dolcetta, Mean field games: Numerical methods for the planning problem,, SIAM J. Control Opt., 50 (2012), 77.
doi: 10.1137/100790069. |
[4] |
F. Cagnetti, D. Gomes and H. V. Tran, Adjoint methods for obstacle problems and weakly coupled systems of PDE,, submitted., (). Google Scholar |
[5] |
F. Cagnetti, D. Gomes and H. V. Tran, Aubry-Mather measures in the non convex setting,, submitted., (). Google Scholar |
[6] |
Lawrence C. Evans and Charles K. Smart, Adjoint methods for the infinity Laplacian partial differential equation,, Arch. Ration. Mech. Anal., 201 (2011), 87.
doi: 10.1007/s00205-011-0399-x. |
[7] |
Lawrence C. Evans, Some new PDE methods for weak KAM theory,, Calc. Var. Partial Differential Equations, 17 (2003), 159.
doi: 10.1007/s00526-002-0164-y. |
[8] |
Lawrence C. Evans, Further PDE methods for weak KAM theory,, Calc. Var. Partial Differential Equations, 35 (2009), 435.
doi: 10.1007/s00526-008-0214-1. |
[9] |
L. C. Evans, Adjoint and compensated compactness methods for Hamilton-Jacobi PDE,, Arch. Ration. Mech. Anal., 197 (2010), 1053.
doi: 10.1007/s00205-010-0307-9. |
[10] |
A. Fathi, Solutions KAM faibles conjuguées et barrières de Peierls,, C. R. Acad. Sci. Paris Sér. I Math., 325 (1997), 649.
doi: 10.1016/S0764-4442(97)84777-5. |
[11] |
A. Fathi, Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens,, C. R. Acad. Sci. Paris Sér. I Math., 324 (1997), 1043.
|
[12] |
A. Fathi, Orbite hétéroclines et ensemble de Peierls,, C. R. Acad. Sci. Paris Sér. I Math., 326 (1998), 1213.
|
[13] |
A. Fathi, Sur la convergence du semi-groupe de Lax-Oleinik,, C. R. Acad. Sci. Paris Sér. I Math., 327 (1998), 267.
doi: 10.1016/S0764-4442(98)80144-4. |
[14] |
D. 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.
|
[15] |
D. Gomes, J. Mohr and R. R. Souza, Mean-field limit of a continuous time finite state game,, preprint, (2011). Google Scholar |
[16] |
D. Gomes, A stochastic analogue of Aubry-Mather theory,, Nonlinearity, 15 (2002), 581.
doi: 10.1088/0951-7715/15/3/304. |
[17] |
D. Gomes and H Sanchez-Morgado, On the stochastic Evans-Aronsson problem,, preprint, (2011). Google Scholar |
[18] |
O. Gueant, "Mean Field Games and Applications to Economics,", Ph.D. Thesis, (2009). Google Scholar |
[19] |
O. Gueant, A reference case for mean field games models,, J. Math. Pures Appl. (9), 92 (2009), 276.
|
[20] |
Minyi Huang, Peter E. Caines and Roland P. Malhamé, Large-population cost-coupled LQG problems with nonuniform agents: Individual-mass behavior and decentralized $\epsilon$-Nash equilibria,, IEEE Trans. Automat. Control, 52 (2007), 1560.
doi: 10.1109/TAC.2007.904450. |
[21] |
Minyi Huang, Roland P. Malhamé and Peter E. Caines, Large population stochastic dynamic games: Closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle,, Commun. Inf. Syst., 6 (2006), 221.
|
[22] |
Jean-Michel Lasry and Pierre-Louis Lions, Jeux à champ moyen. I. Le cas stationnaire,, C. R. Math. Acad. Sci. Paris, 343 (2006), 619.
doi: 10.1016/j.crma.2006.09.019. |
[23] |
Jean-Michel Lasry and Pierre-Louis Lions, Jeux à champ moyen. II. Horizon fini et contrôle optimal,, C. R. Math. Acad. Sci. Paris, 343 (2006), 679.
doi: 10.1016/j.crma.2006.09.018. |
[24] |
Jean-Michel Lasry and Pierre-Louis Lions, Mean field games,, Jpn. J. Math., 2 (2007), 229.
|
[25] |
Jean-Michel Lasry and Pierre-Louis Lions, "Mean Field Games,", Cahiers de la Chaire Finance et Développement Durable, (2007).
|
[26] |
Jean-Michel Lasry, Pierre-Louis Lions and O. Guéant, Application of mean field games to growth theory,, preprint, (2010). Google Scholar |
[27] |
Jean-Michel Lasry, Pierre-Louis Lions and O. Guéant, Mean field games and applications,, in, 2003 (2011), 205.
|
[28] |
J. Mather, Action minimizing invariant measure for positive definite Lagrangian systems,, Math. Z, 207 (1991), 169.
doi: 10.1007/BF02571383. |
[29] |
Ricardo Mañé, On the minimizing measures of Lagrangian dynamical systems,, Nonlinearity, 5 (1992), 623.
|
[30] |
Kaizhi Wang, Action minimizing stochastic invariant measures for a class of Lagrangian systems,, Commun. Pure Appl. Anal., 7 (2008), 1211.
|
show all references
References:
[1] |
Y. Achdou and I. Capuzzo-Dolcetta, Mean field games: Numerical methods,, SIAM J. Numer. Anal., 48 (2010), 1136.
doi: 10.1137/090758477. |
[2] |
Julien Salomon, Aimée Lachapelle and Gabriel Turinici, Computation of mean field equilibria in economics,, Math. Models Methods Appl. Sci., 20 (2010), 567.
doi: 10.1142/S0218202510004349. |
[3] |
F. Camilli, Y. Achdou and I. Capuzzo-Dolcetta, Mean field games: Numerical methods for the planning problem,, SIAM J. Control Opt., 50 (2012), 77.
doi: 10.1137/100790069. |
[4] |
F. Cagnetti, D. Gomes and H. V. Tran, Adjoint methods for obstacle problems and weakly coupled systems of PDE,, submitted., (). Google Scholar |
[5] |
F. Cagnetti, D. Gomes and H. V. Tran, Aubry-Mather measures in the non convex setting,, submitted., (). Google Scholar |
[6] |
Lawrence C. Evans and Charles K. Smart, Adjoint methods for the infinity Laplacian partial differential equation,, Arch. Ration. Mech. Anal., 201 (2011), 87.
doi: 10.1007/s00205-011-0399-x. |
[7] |
Lawrence C. Evans, Some new PDE methods for weak KAM theory,, Calc. Var. Partial Differential Equations, 17 (2003), 159.
doi: 10.1007/s00526-002-0164-y. |
[8] |
Lawrence C. Evans, Further PDE methods for weak KAM theory,, Calc. Var. Partial Differential Equations, 35 (2009), 435.
doi: 10.1007/s00526-008-0214-1. |
[9] |
L. C. Evans, Adjoint and compensated compactness methods for Hamilton-Jacobi PDE,, Arch. Ration. Mech. Anal., 197 (2010), 1053.
doi: 10.1007/s00205-010-0307-9. |
[10] |
A. Fathi, Solutions KAM faibles conjuguées et barrières de Peierls,, C. R. Acad. Sci. Paris Sér. I Math., 325 (1997), 649.
doi: 10.1016/S0764-4442(97)84777-5. |
[11] |
A. Fathi, Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens,, C. R. Acad. Sci. Paris Sér. I Math., 324 (1997), 1043.
|
[12] |
A. Fathi, Orbite hétéroclines et ensemble de Peierls,, C. R. Acad. Sci. Paris Sér. I Math., 326 (1998), 1213.
|
[13] |
A. Fathi, Sur la convergence du semi-groupe de Lax-Oleinik,, C. R. Acad. Sci. Paris Sér. I Math., 327 (1998), 267.
doi: 10.1016/S0764-4442(98)80144-4. |
[14] |
D. 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.
|
[15] |
D. Gomes, J. Mohr and R. R. Souza, Mean-field limit of a continuous time finite state game,, preprint, (2011). Google Scholar |
[16] |
D. Gomes, A stochastic analogue of Aubry-Mather theory,, Nonlinearity, 15 (2002), 581.
doi: 10.1088/0951-7715/15/3/304. |
[17] |
D. Gomes and H Sanchez-Morgado, On the stochastic Evans-Aronsson problem,, preprint, (2011). Google Scholar |
[18] |
O. Gueant, "Mean Field Games and Applications to Economics,", Ph.D. Thesis, (2009). Google Scholar |
[19] |
O. Gueant, A reference case for mean field games models,, J. Math. Pures Appl. (9), 92 (2009), 276.
|
[20] |
Minyi Huang, Peter E. Caines and Roland P. Malhamé, Large-population cost-coupled LQG problems with nonuniform agents: Individual-mass behavior and decentralized $\epsilon$-Nash equilibria,, IEEE Trans. Automat. Control, 52 (2007), 1560.
doi: 10.1109/TAC.2007.904450. |
[21] |
Minyi Huang, Roland P. Malhamé and Peter E. Caines, Large population stochastic dynamic games: Closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle,, Commun. Inf. Syst., 6 (2006), 221.
|
[22] |
Jean-Michel Lasry and Pierre-Louis Lions, Jeux à champ moyen. I. Le cas stationnaire,, C. R. Math. Acad. Sci. Paris, 343 (2006), 619.
doi: 10.1016/j.crma.2006.09.019. |
[23] |
Jean-Michel Lasry and Pierre-Louis Lions, Jeux à champ moyen. II. Horizon fini et contrôle optimal,, C. R. Math. Acad. Sci. Paris, 343 (2006), 679.
doi: 10.1016/j.crma.2006.09.018. |
[24] |
Jean-Michel Lasry and Pierre-Louis Lions, Mean field games,, Jpn. J. Math., 2 (2007), 229.
|
[25] |
Jean-Michel Lasry and Pierre-Louis Lions, "Mean Field Games,", Cahiers de la Chaire Finance et Développement Durable, (2007).
|
[26] |
Jean-Michel Lasry, Pierre-Louis Lions and O. Guéant, Application of mean field games to growth theory,, preprint, (2010). Google Scholar |
[27] |
Jean-Michel Lasry, Pierre-Louis Lions and O. Guéant, Mean field games and applications,, in, 2003 (2011), 205.
|
[28] |
J. Mather, Action minimizing invariant measure for positive definite Lagrangian systems,, Math. Z, 207 (1991), 169.
doi: 10.1007/BF02571383. |
[29] |
Ricardo Mañé, On the minimizing measures of Lagrangian dynamical systems,, Nonlinearity, 5 (1992), 623.
|
[30] |
Kaizhi Wang, Action minimizing stochastic invariant measures for a class of Lagrangian systems,, Commun. Pure Appl. Anal., 7 (2008), 1211.
|
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