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This work introduces a new general approach for the numerical analysis of stable equilibria to second order mean field games systems in cases where the uniqueness of solutions may fail.
“Finite Dimensional Approximation of Nonlinear Problems: Part I: Branches of Nonsingular Solutions”
F. Brezzi, J. Rappaz and P.. Raviart · 1980
Earlier work this paper cites.
“Finite Element Methods for Navier-Stokes Equations” 5
Vivette Girault and Pierre-Arnaud Raviart · 1986
Earlier work this paper cites.
“Nonlinear superposition operators” 95
J\"urgen Appell and Petr. Zabrejko · 1990
Earlier work this paper cites.
“On numerical approximation in bifurcation theory” 13
Michel Crouzeix and Jacques Rappaz · 1990
Earlier work this paper cites.
“Further Remarks on the Nemitskii Operator in Hölder Spaces”
Rita Nugari · 1993
Earlier work this paper cites.
“Nonlinear Functional Analysis and Its Applications: Fixed-point Theorems”
Eberhard Zeidler · 1993
Earlier work this paper cites.
“Numerical analysis for nonlinear and bifurcation problems”
Gabriel Caloz and Jacques Rappaz · 1997
Earlier work this paper cites.
“Stochastic Controls”
Jiongmin Yong and Xun Zhou · 1999
Earlier work this paper cites.
“Elliptic Partial Differential Equations of Second Order” 224
David Gilbarg and Neil. Trudinger · 2001
Earlier work this paper cites.
“Theory and Practice of Finite Elements” 159
S.. Antman, J.. Marsden and L. Sirovich · 2004
Earlier work this paper cites.
“Controlled Markov Processes and Viscosity Solutions”
Wendell Fleming and Halil Soner · 2006
Earlier work this paper cites.
“Large Population Stochastic Dynamic Games: Closed-Loop McKean-Vlasov Systems and the Nash Certainty Equivalence Principle”
Minyi Huang, Roland Malhamé and Peter Caines · 2006
Earlier work this paper cites.
“Jeux à champ moyen. I – Le cas stationnaire”
Jean-Michel Lasry and Pierre-Louis Lions · 2006
Earlier work this paper cites.
“Jeux à champ moyen. II – Horizon fini et contrôle optimal”
Jean-Michel Lasry and Pierre-Louis Lions · 2006
Earlier work this paper cites.
“Large-Population Cost-Coupled LQG Problems With Nonuniform Agents: Individual-Mass Behavior and Decentralized ε \varepsilon -Nash Equilibria”
Minyi Huang, Peter. Caines and Roland. Malhame · 2007
Earlier work this paper cites.
“Mean Field Games”
Jean-Michel Lasry and Pierre-Louis Lions · 2007
Earlier work this paper cites.
“Cours Au Collège de France.”, 2007
Pierre-Louis Lions · 2007
Cited alongside, same era.
“The Mathematical Theory of Finite Element Methods” 15
J.. Marsden, L. Sirovich and S.. Antman · 2008
Cited alongside, same era.
“Optimization with PDE Constraints” 23
Michael Hinze, Rene Pinnau, Michael Ulbrich and Stefan Ulbrich · 2009
Cited alongside, same era.
“A first course in Sobolev spaces” 105
Giovanni Leoni · 2009
Cited alongside, same era.
“Functional analysis, Sobolev spaces and partial differential equations”, Universitext
Haim Brezis · 2011
Cited alongside, same era.
“Deterministic and Stochastic Optimal Control”
Wendell Fleming and Raymond Rishel · 2012
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“On the existence of oscillating solutions in non-monotone mean-field games”
Marco Cirant · 2018
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“Existence of weak solutions to stationary mean-field games through variational inequalities”
Rita Ferreira and Diogo Gomes · 2018
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“Interpolation Theory”
Alessandra Lunardi · 2018
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“On non-uniqueness and uniqueness of solutions in finite-horizon mean field games”
Martino Bardi and Markus Fischer · 2019
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“The Master Equation and the Convergence Problem in Mean Field Games”
Pierre Cardaliaguet, François Delarue, Jean-Michel Lasry and Pierre-Louis Lions · 2019
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“Time-dependent focusing mean-field games: the sub-critical case”
Marco Cirant and Daniela Tonon · 2019
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Yves Achdou, Guy Barles, Hitoshi Ishii and Grigory. Litvinov · 2013
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“Mean Field Games: Convergence of a Finite Difference Method”
Yves Achdou, Fabio Camilli and Italo Capuzzo-Dolcetta · 2013
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“Mean Field Games and Mean Field Type Control Theory”, SpringerBriefs in Mathematics
Alain Bensoussan, Jens Frehse and Phillip Yam · 2013
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“Implicit Functions and Solution Mappings: A View from Variational Analysis”, Springer Series in Operations Research and Financial Engineering
Asen. Dontchev and R. Rockafellar · 2014
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“Mean Field Games Models—A Brief Survey”
Diogo. Gomes and João Saúde · 2014
Cited alongside, same era.
“Fokker–Planck–Kolmogorov Equations” 207
Vladimir Bogachev, Nicolai Krylov, Michael Röckner and Stanislav Shaposhnikov · 2015
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Cham: Springer International Publishing, 2020
“Mean Field Games: Cetraro, Italy 2019” 2281 · 2020
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“The selection problem for some first-order stationary mean-field games”
Diogo. Gomes, Hiroyoshi Mitake and Kengo Terai · 2020
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“Error Estimates of a Theta-Scheme for Second-Order Mean Field Games”
J.édéric Bonnans, Kang Liu and Laurent Pfeiffer · 2023
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“Generic properties of first-order mean field games”
Alberto Bressan and Khai. Nguyen · 2023
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Yohance A.. Osborne and Iain Smears · 2023
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“On the Quadratic Convergence of Newton’s Method for Mean Field Games with Non-separable Hamiltonian”
Fabio Camilli and Qing Tang · 2024
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“Analysis and Numerical Approximation of Stationary Second-Order Mean Field Game Partial Differential Inclusions”
Yohance A.. Osborne and Iain Smears · 2024
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Yohance A.. Osborne and Iain Smears · 2024
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“Learning Optimal Policies in Potential Mean Field Games: Smoothed Policy Iteration Algorithms”
Qing Tang and Jiahao Song · 2024
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