-
Previous Article
A modest proposal for MFG with density constraints
- NHM Home
- This Issue
-
Next Article
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 |
[1] |
Marco Cirant, Diogo A. Gomes, Edgard A. Pimentel, Héctor Sánchez-Morgado. On some singular mean-field games. Journal of Dynamics & Games, 2021 doi: 10.3934/jdg.2021006 |
[2] |
Sandrine Anthoine, Jean-François Aujol, Yannick Boursier, Clothilde Mélot. Some proximal methods for Poisson intensity CBCT and PET. Inverse Problems & Imaging, 2012, 6 (4) : 565-598. doi: 10.3934/ipi.2012.6.565 |
[3] |
Seung-Yeal Ha, Jinwook Jung, Jeongho Kim, Jinyeong Park, Xiongtao Zhang. A mean-field limit of the particle swarmalator model. Kinetic & Related Models, , () : -. doi: 10.3934/krm.2021011 |
[4] |
Hong Seng Sim, Wah June Leong, Chuei Yee Chen, Siti Nur Iqmal Ibrahim. Multi-step spectral gradient methods with modified weak secant relation for large scale unconstrained optimization. Numerical Algebra, Control & Optimization, 2018, 8 (3) : 377-387. doi: 10.3934/naco.2018024 |
[5] |
Marcel Braukhoff, Ansgar Jüngel. Entropy-dissipating finite-difference schemes for nonlinear fourth-order parabolic equations. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3335-3355. doi: 10.3934/dcdsb.2020234 |
[6] |
Tomáš Roubíček. An energy-conserving time-discretisation scheme for poroelastic media with phase-field fracture emitting waves and heat. Discrete & Continuous Dynamical Systems - S, 2017, 10 (4) : 867-893. doi: 10.3934/dcdss.2017044 |
[7] |
Hakan Özadam, Ferruh Özbudak. A note on negacyclic and cyclic codes of length $p^s$ over a finite field of characteristic $p$. Advances in Mathematics of Communications, 2009, 3 (3) : 265-271. doi: 10.3934/amc.2009.3.265 |
[8] |
Qigang Yuan, Jingli Ren. Periodic forcing on degenerate Hopf bifurcation. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2857-2877. doi: 10.3934/dcdsb.2020208 |
[9] |
Junichi Minagawa. On the uniqueness of Nash equilibrium in strategic-form games. Journal of Dynamics & Games, 2020, 7 (2) : 97-104. doi: 10.3934/jdg.2020006 |
[10] |
Michael Grinfeld, Amy Novick-Cohen. Some remarks on stability for a phase field model with memory. Discrete & Continuous Dynamical Systems, 2006, 15 (4) : 1089-1117. doi: 10.3934/dcds.2006.15.1089 |
[11] |
Zhigang Pan, Chanh Kieu, Quan Wang. Hopf bifurcations and transitions of two-dimensional Quasi-Geostrophic flows. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021025 |
[12] |
Yahui Niu. A Hopf type lemma and the symmetry of solutions for a class of Kirchhoff equations. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021027 |
[13] |
Caifang Wang, Tie Zhou. The order of convergence for Landweber Scheme with $\alpha,\beta$-rule. Inverse Problems & Imaging, 2012, 6 (1) : 133-146. doi: 10.3934/ipi.2012.6.133 |
[14] |
Raghda A. M. Attia, Dumitru Baleanu, Dianchen Lu, Mostafa M. A. Khater, El-Sayed Ahmed. Computational and numerical simulations for the deoxyribonucleic acid (DNA) model. Discrete & Continuous Dynamical Systems - S, 2021 doi: 10.3934/dcdss.2021018 |
[15] |
Arseny Egorov. Morse coding for a Fuchsian group of finite covolume. Journal of Modern Dynamics, 2009, 3 (4) : 637-646. doi: 10.3934/jmd.2009.3.637 |
[16] |
Wolf-Jüergen Beyn, Janosch Rieger. The implicit Euler scheme for one-sided Lipschitz differential inclusions. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 409-428. doi: 10.3934/dcdsb.2010.14.409 |
[17] |
Alina Chertock, Alexander Kurganov, Mária Lukáčová-Medvi${\rm{\check{d}}}$ová, Șeyma Nur Özcan. An asymptotic preserving scheme for kinetic chemotaxis models in two space dimensions. Kinetic & Related Models, 2019, 12 (1) : 195-216. doi: 10.3934/krm.2019009 |
[18] |
Hailing Xuan, Xiaoliang Cheng. Numerical analysis and simulation of an adhesive contact problem with damage and long memory. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2781-2804. doi: 10.3934/dcdsb.2020205 |
[19] |
Vieri Benci, Marco Cococcioni. The algorithmic numbers in non-archimedean numerical computing environments. Discrete & Continuous Dynamical Systems - S, 2021, 14 (5) : 1673-1692. doi: 10.3934/dcdss.2020449 |
[20] |
Vakhtang Putkaradze, Stuart Rogers. Numerical simulations of a rolling ball robot actuated by internal point masses. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 143-207. doi: 10.3934/naco.2020021 |
2019 Impact Factor: 1.053
Tools
Metrics
Other articles
by authors
[Back to Top]