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Volumn 14, Issue 3, 2019, Pages 537-566

A class of infinite horizon mean field games on networks

Author keywords

Ergodic problems; Kirchhoff conditions; Mean field games; Networks

Indexed keywords

DYNAMIC PROGRAMMING; NETWORKS (CIRCUITS); STOCHASTIC SYSTEMS;

EID: 85068609345     PISSN: 15561801     EISSN: 1556181X     Source Type: Journal    
DOI: 10.3934/nhm.2019021     Document Type: Article
Times cited : (9)

References (35)
  • 1
    • 84883178689 scopus 로고    scopus 로고
    • Finite difference methods for mean field games, in Hamilton-Jacobi Equations: Approximations, Numerical Analysis And Applications
    • Springer, Heidelberg, 2013
    • Y. Achdou Finite difference methods for mean field games, in Hamilton-Jacobi Equations: Approximations, Numerical Analysis And Applications, Lecture Notes in Mathematics, 2074, Springer, Heidelberg, 2013, 1-47
    • Lecture Notes in Mathematics , Issue.2074 , pp. 1-47
    • Achdou, Y.1
  • 4
    • 84930903523 scopus 로고    scopus 로고
    • Hamilton-Jacobi equations for optimal control on junc-tions and networks
    • Y. Achdou, S. Oudet and N. Tchou Hamilton-Jacobi equations for optimal control on junc-tions and networks, ESAIM Control Optim. Calc. Var., 21 (2015), 876-899
    • (2015) ESAIM Control Optim. Calc. Var , vol.21 , pp. 876-899
    • Achdou, Y.1    Oudet, S.2    Tchou, N.3
  • 5
    • 84960841215 scopus 로고    scopus 로고
    • Convergence of a finite difference scheme to weak solutions of the system of partial differential equation arising in mean field games
    • Y. Achdou and A. Porretta Convergence of a finite difference scheme to weak solutions of the system of partial differential equation arising in mean field games, SIAM J. Numer. Anal., 54 (2016), 161-186
    • (2016) SIAM J. Numer. Anal , vol.54 , pp. 161-186
    • Achdou, Y.1    Porretta, A.2
  • 7
    • 84964879680 scopus 로고    scopus 로고
    • Stationary mean field games systems defined on networks
    • F. Camilli and C. Marchi Stationary mean field games systems defined on networks, SIAM J. Control Optim., 54 (2016), 1085-1103
    • (2016) SIAM J. Control Optim , vol.54 , pp. 1085-1103
    • Camilli, F.1    Marchi, C.2
  • 8
    • 84875061425 scopus 로고    scopus 로고
    • The vanishing viscosity limit for Hamilton-Jacobi equations on networks
    • F. Camilli, C. Marchi and D. Schieborn The vanishing viscosity limit for Hamilton-Jacobi equations on networks, J. Differential Equations, 254 (2013), 4122-4143
    • (2013) J. Differential Equations , vol.254 , pp. 4122-4143
    • Camilli, F.1    Marchi, C.2    Schieborn, D.3
  • 11
    • 85068597476 scopus 로고    scopus 로고
    • Ph.D. thesis
    • M.-K. Dao Ph.D. thesis, 2018
    • (2018)
    • Dao, M.-K.1
  • 13
    • 27144535622 scopus 로고    scopus 로고
    • Theory and Practice of Finite Elements
    • Springer-Verlag, New York
    • A. Ern and J.-L. Guermond Theory and Practice of Finite Elements, Applied Mathematical Sciences, 159, Springer-Verlag, New York, 2004
    • (2004) Applied Mathematical Sciences , vol.159
    • Ern, A.1    Guermond, J.-L.2
  • 14
    • 85006964129 scopus 로고    scopus 로고
    • Homogenization of second order discrete model with local perturbation and application to traffic flow
    • N. Forcadel, W. Salazar and M. Zaydan Homogenization of second order discrete model with local perturbation and application to traffic flow, Discrete Contin. Dyn. Syst., 37 (2017), 1437-1487
    • (2017) Discrete Contin. Dyn. Syst , vol.37 , pp. 1437-1487
    • Forcadel, N.1    Salazar, W.2    Zaydan, M.3
  • 15
    • 0034387537 scopus 로고    scopus 로고
    • Diffusion processes on graphs: Stochastic differential equations large deviation principle
    • M. I. Freidlin and S.-J. Sheu Diffusion processes on graphs: Stochastic differential equations, large deviation principle, Probab. Theory Related Fields, 116 (2000), 181-220
    • (2000) Probab. Theory Related Fields , vol.116 , pp. 181-220
    • Freidlin, M.I.1    Sheu, S.-J.2
  • 16
    • 0000828252 scopus 로고
    • Diffusion processes on graphs and the averaging principle
    • M. I. Freidlin and A. D. Wentzell Diffusion processes on graphs and the averaging principle, Ann. Probab., 21 (1993), 2215-2245
    • (1993) Ann. Probab , vol.21 , pp. 2215-2245
    • Freidlin, M.I.1    Wentzell, A.D.2
  • 18
    • 0003549965 scopus 로고    scopus 로고
    • Elliptic Partial Differential Equations of Second Order, Reprint of the 1998 edition
    • Springer-Verlag, Berlin
    • D. Gilbarg and N. S. Trudinger Elliptic Partial Differential Equations of Second Order, Reprint of the 1998 edition, Classics in Mathematics, Springer-Verlag, Berlin, 2001
    • (2001) Classics in Mathematics
    • Gilbarg, D.1    Trudinger, N.S.2
  • 19
    • 84892860445 scopus 로고    scopus 로고
    • On the existence of classical solutions for stationary extended mean field games
    • D. A. Gomes, S. Patrizi and V. Voskanyan On the existence of classical solutions for stationary extended mean field games, Nonlinear Anal., 99 (2014), 49-79
    • (2014) Nonlinear Anal , vol.99 , pp. 49-79
    • Gomes, D.A.1    Patrizi, S.2    Voskanyan, V.3
  • 20
    • 84978423911 scopus 로고    scopus 로고
    • Local regularity for mean-field games in the whole space
    • D. A. Gomes and E. Pimentel Local regularity for mean-field games in the whole space, Minimax Theory Appl., 1 (2016), 65-82
    • (2016) Minimax Theory Appl , vol.1 , pp. 65-82
    • Gomes, D.A.1    Pimentel, E.2
  • 22
    • 77958476920 scopus 로고    scopus 로고
    • Mean field games and applications, in Paris-Princeton Lectures on Mathematical Finance 2010
    • Springer, Berlin, 2011
    • O. Guéant, J.-M. Lasry and P.-L. Lions Mean field games and applications, in Paris-Princeton Lectures on Mathematical Finance 2010, Lecture Notes in Mathematics, 2003, Springer, Berlin, 2011, 205-266
    • (2003) Lecture Notes in Mathematics , pp. 205-266
    • Guéant, O.1    Lasry, J.-M.2    Lions, P.-L.3
  • 23
    • 34249075491 scopus 로고    scopus 로고
    • An invariance principle in large population stochastic dynamic games
    • M. Huang, P. E. Caines and R. P. Malhamé An invariance principle in large population stochastic dynamic games, J. Syst. Sci. Complex., 20 (2007), 162-172
    • (2007) J. Syst. Sci. Complex , vol.20 , pp. 162-172
    • Huang, M.1    Caines, P.E.2    Malhamé, R.P.3
  • 24
    • 34648831837 scopus 로고    scopus 로고
    • Large-population cost-coupled LQG problems with nonuniform agents: Individual-mass behavior and decentralized ψ-Nash equilibria
    • M. Huang, P. E. Caines and R. P. Malhamé Large-population cost-coupled LQG problems with nonuniform agents: Individual-mass behavior and decentralized ψ-Nash equilibria, IEEE Trans. Automat. Control, 52 (2007), 1560-1571
    • (2007) IEEE Trans. Automat. Control , vol.52 , pp. 1560-1571
    • Huang, M.1    Caines, P.E.2    Malhamé, R.P.3
  • 25
    • 39549087376 scopus 로고    scopus 로고
    • Large population stochastic dynamic games: Closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle
    • M. Huang, R. P. Malhamé and P. E. Caines Large population stochastic dynamic games: Closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle, Commun. Inf. Syst., 6 (2006), 221-251
    • (2006) Commun. Inf. Syst , vol.6 , pp. 221-251
    • Huang, M.1    Malhamé, R.P.2    Caines, P.E.3
  • 26
    • 84873895024 scopus 로고    scopus 로고
    • A Hamilton-Jacobi approach to junction problems and application to traffic ows
    • C. Imbert, R. Monneau and H. Zidani A Hamilton-Jacobi approach to junction problems and application to traffic ows, ESAIM Control Optim. Calc. Var., 19 (2013), 129-166
    • (2013) ESAIM Control Optim. Calc. Var , vol.19 , pp. 129-166
    • Imbert, C.1    Monneau, R.2    Zidani, H.3
  • 27
    • 85020603522 scopus 로고    scopus 로고
    • Flux-limited solutions for quasi-convex Hamilton-Jacobi equa-tions on networks
    • C. Imbert and R. Monneau Flux-limited solutions for quasi-convex Hamilton-Jacobi equa-tions on networks, Ann. Sci. Ec. Norm. Super., 50 (2017), 357-448
    • (2017) Ann. Sci. Ec. Norm. Super , vol.50 , pp. 357-448
    • Imbert, C.1    Monneau, R.2
  • 29
    • 33751077273 scopus 로고    scopus 로고
    • Jeuxa champ moyen. II. Horizon fini et contr^ole optimal
    • J.-M. Lasry and P.-L. Lions Jeuxa champ moyen. II. Horizon fini et contr^ole optimal, C. R. Math. Acad. Sci. Paris, 343 (2006), 679-684
    • (2006) C. R. Math. Acad. Sci. Paris , vol.343 , pp. 679-684
    • Lasry, J.-M.1    Lions, P.-L.2
  • 32
    • 85035344029 scopus 로고    scopus 로고
    • Well-posedness for multi-dimensional junction problems with Kirchoff-type conditions
    • P.-L. Lions and P. Souganidis Well-posedness for multi-dimensional junction problems with Kirchoff-type conditions, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl., 28 (2017), 807-816
    • (2017) Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl , vol.28 , pp. 807-816
    • Lions, P.-L.1    Souganidis, P.2
  • 33
    • 84925014244 scopus 로고    scopus 로고
    • Weak solutions to Fokker-Planck equations and mean field games
    • A. Porretta Weak solutions to Fokker-Planck equations and mean field games, Arch. Rational Mech. Anal., 216 (2015), 1-62
    • (2015) Arch. Rational Mech. Anal , vol.216 , pp. 1-62
    • Porretta, A.1
  • 34
    • 85028676686 scopus 로고    scopus 로고
    • On the weak theory for mean field games systems
    • A. Porretta On the weak theory for mean field games systems, Boll. U.M.I., 10 (2017), 411-439
    • (2017) Boll. U.M.I , vol.10 , pp. 411-439
    • Porretta, A.1
  • 35
    • 0000231942 scopus 로고
    • Classical solvability of linear parabolic equations on networks
    • J. von Below Classical solvability of linear parabolic equations on networks, J. Differential Equations, 72 (1988), 316-337
    • (1988) J. Differential Equations , vol.72 , pp. 316-337
    • von Below, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.