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Iterative strategies for solving linearized discrete mean field games systems
From discrete to continuous Wardrop equilibria
1. | Laboratoire Marin Mersenne, Université Paris I, 90 rue de Tolbiac, 75013, Paris, France |
2. | CEREMADE, UMR CNRS 7534, Université Paris-Dauphine, Pl. de Lattre de Tassigny, 75775 Paris Cedex 16 |
References:
[1] |
J.-B. Baillon and R. Cominetti, Markovian traffic equilibrium,, Math. Prog., 111 (2008), 33.
doi: 10.1007/s10107-006-0076-2. |
[2] |
M. Beckmann, C. McGuire and C. Winsten, "Studies in Economics of Transportation,", Yale University Press, (1956). Google Scholar |
[3] |
F. Benmansour, G. Carlier, G. Peyré and F. Santambrogio, Numerical approximation of continuous traffic congestion equilibria,, Netw. Heterog. Media, 4 (2009), 605.
|
[4] |
A. Braides, "$\Gamma$-Convergence for Beginners,", Oxford Lecture Series in Mathematics and its Applications, 22 (2002).
|
[5] |
L. Brasco, G. Carlier and F. Santambrogio, Congested traffic dynamics, weak flows and very degenerate elliptic equations,, Journal de Mathématiques Pures et Appliquées (9), 93 (2010), 652.
|
[6] |
G. Carlier, C. Jimenez and F. Santambrogio, Optimal transportation with traffic congestion and Wardrop equilibria,, SIAM J. Control Optim., 47 (2008), 1330.
doi: 10.1137/060672832. |
[7] |
G. Dal Maso, "An Introduction to $\Gamma-$Convergence,", Progress in Nonlinear Differential Equations and their Applications, 8 (1993).
|
[8] |
C. Villani, "Topics in Optimal Transportation,", Graduate Studies in Mathematics, 58 (2003).
|
[9] |
J. G. Wardrop, Some theoretical aspects of road traffic research,, Proc. Inst. Civ. Eng., 2 (1952), 325. Google Scholar |
show all references
References:
[1] |
J.-B. Baillon and R. Cominetti, Markovian traffic equilibrium,, Math. Prog., 111 (2008), 33.
doi: 10.1007/s10107-006-0076-2. |
[2] |
M. Beckmann, C. McGuire and C. Winsten, "Studies in Economics of Transportation,", Yale University Press, (1956). Google Scholar |
[3] |
F. Benmansour, G. Carlier, G. Peyré and F. Santambrogio, Numerical approximation of continuous traffic congestion equilibria,, Netw. Heterog. Media, 4 (2009), 605.
|
[4] |
A. Braides, "$\Gamma$-Convergence for Beginners,", Oxford Lecture Series in Mathematics and its Applications, 22 (2002).
|
[5] |
L. Brasco, G. Carlier and F. Santambrogio, Congested traffic dynamics, weak flows and very degenerate elliptic equations,, Journal de Mathématiques Pures et Appliquées (9), 93 (2010), 652.
|
[6] |
G. Carlier, C. Jimenez and F. Santambrogio, Optimal transportation with traffic congestion and Wardrop equilibria,, SIAM J. Control Optim., 47 (2008), 1330.
doi: 10.1137/060672832. |
[7] |
G. Dal Maso, "An Introduction to $\Gamma-$Convergence,", Progress in Nonlinear Differential Equations and their Applications, 8 (1993).
|
[8] |
C. Villani, "Topics in Optimal Transportation,", Graduate Studies in Mathematics, 58 (2003).
|
[9] |
J. G. Wardrop, Some theoretical aspects of road traffic research,, Proc. Inst. Civ. Eng., 2 (1952), 325. Google Scholar |
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