메뉴 건너뛰기




Volumn 4, Issue 2, 2014, Pages 110-154

Mean Field Games Models-A Brief Survey

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84899464039     PISSN: 21530785     EISSN: 21530793     Source Type: Journal    
DOI: 10.1007/s13235-013-0099-2     Document Type: Article
Times cited : (351)

References (88)
  • 2
    • 77956048120 scopus 로고    scopus 로고
    • Mean field games: numerical methods
    • Achdou Y, Capuzzo-Dolcetta I (2010) Mean field games: numerical methods. SIAM J Numer Anal 48(3): 1136-1162.
    • (2010) SIAM J Numer Anal , vol.48 , Issue.3 , pp. 1136-1162
    • Achdou, Y.1    Capuzzo-Dolcetta, I.2
  • 3
    • 84865566007 scopus 로고    scopus 로고
    • Iterative strategies for solving linearized discrete mean field games systems
    • Achdou Y, Perez V (2012) Iterative strategies for solving linearized discrete mean field games systems. Netw Heterog Media 7(2): 197-217.
    • (2012) Netw Heterog Media , vol.7 , Issue.2 , pp. 197-217
    • Achdou, Y.1    Perez, V.2
  • 4
    • 84858650669 scopus 로고    scopus 로고
    • Mean field games: numerical methods for the planning problem
    • Achdou Y, Camilli F, Capuzzo-Dolcetta I (2012) Mean field games: numerical methods for the planning problem. SIAM J Control Optim 50(1): 77-109.
    • (2012) SIAM J Control Optim , vol.50 , Issue.1 , pp. 77-109
    • Achdou, Y.1    Camilli, F.2    Capuzzo-Dolcetta, I.3
  • 5
    • 7544243351 scopus 로고    scopus 로고
    • Transport equation and Cauchy problem for BV vector fields
    • Ambrosio L (2004) Transport equation and Cauchy problem for BV vector fields. Invent Math 158(2): 227-260.
    • (2004) Invent Math , vol.158 , Issue.2 , pp. 227-260
    • Ambrosio, L.1
  • 6
    • 36949000865 scopus 로고    scopus 로고
    • Transport equation and Cauchy problem for non-smooth vector fields
    • Lecture notes in math, Berlin: Springer
    • Ambrosio L (2008) Transport equation and Cauchy problem for non-smooth vector fields. In: Calculus of variations and nonlinear partial differential equations. Lecture notes in math, vol 1927. Springer, Berlin, pp 1-41.
    • (2008) Calculus of Variations and Nonlinear Partial Differential Equations , vol.1927 , pp. 1-41
    • Ambrosio, L.1
  • 8
    • 84865608369 scopus 로고    scopus 로고
    • Explicit solutions of some linear-quadratic mean field games
    • Bardi M (2012) Explicit solutions of some linear-quadratic mean field games. Netw Heterog Media 7(2): 243-261.
    • (2012) Netw Heterog Media , vol.7 , Issue.2 , pp. 243-261
    • Bardi, M.1
  • 10
    • 84887513526 scopus 로고    scopus 로고
    • The derivation of ergodic mean field game equations for several populations of players
    • (to appear)
    • Bardi M, Feleqi E (2013) The derivation of ergodic mean field game equations for several populations of players. Dyn Games Appl (to appear).
    • (2013) Dyn Games Appl
    • Bardi, M.1    Feleqi, E.2
  • 13
    • 0034407460 scopus 로고    scopus 로고
    • A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
    • Benamou J-D, Brenier Y (2000) A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numer Math 84(3): 375-393.
    • (2000) Numer Math , vol.84 , Issue.3 , pp. 375-393
    • Benamou, J.-D.1    Brenier, Y.2
  • 15
    • 84876190746 scopus 로고    scopus 로고
    • Linear-quadratic mean field games
    • Preprint
    • Bensoussan A, Sung K, Yam S, Yung S (2013) Linear-quadratic mean field games. Preprint.
    • (2013)
    • Bensoussan, A.1    Sung, K.2    Yam, S.3    Yung, S.4
  • 16
    • 84866430071 scopus 로고    scopus 로고
    • An introduction to the Aubry-Mather theory
    • Biryuk A, Gomes DA (2010) An introduction to the Aubry-Mather theory. São Paulo J Math Sci 4(1): 17-63.
    • (2010) São Paulo J Math Sci , vol.4 , Issue.1 , pp. 17-63
    • Biryuk, A.1    Gomes, D.A.2
  • 19
    • 84865538817 scopus 로고    scopus 로고
    • A semi-discrete approximation for a first order mean field game problem
    • Camilli F, Silva F (2012) A semi-discrete approximation for a first order mean field game problem. Netw Heterog Media 7(2): 263-277.
    • (2012) Netw Heterog Media , vol.7 , Issue.2 , pp. 263-277
    • Camilli, F.1    Silva, F.2
  • 29
    • 84876129326 scopus 로고    scopus 로고
    • Control of McKean-Vlasov dynamics versus mean field games
    • Carmona R, Delarue F, Lachapelle A (2013) Control of McKean-Vlasov dynamics versus mean field games. Math Financ Econ 7(2): 131-166.
    • (2013) Math Financ Econ , vol.7 , Issue.2 , pp. 131-166
    • Carmona, R.1    Delarue, F.2    Lachapelle, A.3
  • 31
    • 64749093071 scopus 로고    scopus 로고
    • Further PDE methods for weak KAM theory
    • Evans LC (2009) Further PDE methods for weak KAM theory. Calc Var Partial Differ Equ 35(4): 435-462.
    • (2009) Calc Var Partial Differ Equ , vol.35 , Issue.4 , pp. 435-462
    • Evans, L.C.1
  • 32
    • 0035589103 scopus 로고    scopus 로고
    • Effective Hamiltonians and averaging for Hamiltonian dynamics. I
    • Evans LC, Gomes D (2001) Effective Hamiltonians and averaging for Hamiltonian dynamics. I. Arch Ration Mech Anal 157(1): 1-33.
    • (2001) Arch Ration Mech Anal , vol.157 , Issue.1 , pp. 1-33
    • Evans, L.C.1    Gomes, D.2
  • 35
    • 0041471525 scopus 로고    scopus 로고
    • A stochastic analogue of Aubry-Mather theory
    • Gomes D (2002) A stochastic analogue of Aubry-Mather theory. Nonlinearity 15(3): 581-603.
    • (2002) Nonlinearity , vol.15 , Issue.3 , pp. 581-603
    • Gomes, D.1
  • 36
    • 85038573877 scopus 로고    scopus 로고
    • Duality principles for fully nonlinear elliptic equations
    • Progr nonlinear differential equations appl, Basel: Birkhäuser
    • Gomes D (2005) Duality principles for fully nonlinear elliptic equations. In: Trends in partial differential equations of mathematical physics. Progr nonlinear differential equations appl, vol 61. Birkhäuser, Basel, pp 125-136.
    • (2005) Trends in Partial Differential Equations of Mathematical Physics , vol.61 , pp. 125-136
    • Gomes, D.1
  • 37
    • 84899428969 scopus 로고    scopus 로고
    • Lagrangian dynamics and a weak KAM theorem on the d-infinite dimensional torus
    • Gomes D, Nurbekyan L (2012) Lagrangian dynamics and a weak KAM theorem on the d-infinite dimensional torus. Dokl Natl Akad Nauk Armen 112(2): 152-159.
    • (2012) Dokl Natl Akad Nauk Armen , vol.112 , Issue.2 , pp. 152-159
    • Gomes, D.1    Nurbekyan, L.2
  • 43
    • 34447498638 scopus 로고    scopus 로고
    • Entropy penalization methods for Hamilton-Jacobi equations
    • Gomes D, Valdinoci E (2007) Entropy penalization methods for Hamilton-Jacobi equations. Adv Math 215(1): 94-152.
    • (2007) Adv Math , vol.215 , Issue.1 , pp. 94-152
    • Gomes, D.1    Valdinoci, E.2
  • 45
  • 46
    • 77549085949 scopus 로고    scopus 로고
    • Discrete time, finite state space mean field games
    • Gomes D, Mohr J, Souza RR (2010) Discrete time, finite state space mean field games. J Math Pures Appl 93(2): 308-328.
    • (2010) J Math Pures Appl , vol.93 , Issue.2 , pp. 308-328
    • Gomes, D.1    Mohr, J.2    Souza, R.R.3
  • 47
    • 79959767868 scopus 로고    scopus 로고
    • The Mather measure and a large deviation principle for the entropy penalized method
    • Gomes D, Lopes A, Mohr J (2011) The Mather measure and a large deviation principle for the entropy penalized method. Commun Contemp Math 13(2): 235-268.
    • (2011) Commun Contemp Math , vol.13 , Issue.2 , pp. 235-268
    • Gomes, D.1    Lopes, A.2    Mohr, J.3
  • 49
    • 84880206151 scopus 로고    scopus 로고
    • Continuous time finite state mean field games
    • Gomes DA, Mohr J, Souza RR (2013) Continuous time finite state mean field games. Appl Math Optim 68(1): 99-143.
    • (2013) Appl Math Optim , vol.68 , Issue.1 , pp. 99-143
    • Gomes, D.A.1    Mohr, J.2    Souza, R.R.3
  • 54
    • 68849084877 scopus 로고    scopus 로고
    • A reference case for mean field games models
    • Gueant O (2009) A reference case for mean field games models. J Math Pures Appl 92(3): 276-294.
    • (2009) J Math Pures Appl , vol.92 , Issue.3 , pp. 276-294
    • Gueant, O.1
  • 58
    • 79952140932 scopus 로고    scopus 로고
    • Large-population LQG games involving a major player: the Nash certainty equivalence principle
    • Huang M (2009/10) Large-population LQG games involving a major player: the Nash certainty equivalence principle. SIAM J Control Optim 48(5): 3318-3353.
    • (2009) SIAM J Control Optim , vol.48 , Issue.5 , pp. 3318-3353
    • Huang, M.1
  • 59
    • 84881146148 scopus 로고    scopus 로고
    • Mean field stochastic games with discrete states and mixed players
    • Vancouver
    • Huang M (2012) Mean field stochastic games with discrete states and mixed players. In: Proc GameNets, Vancouver.
    • (2012) Proc GameNets
    • Huang, M.1
  • 60
    • 39549087376 scopus 로고    scopus 로고
    • Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle
    • Huang M, Malhamé RP, Caines PE (2006) Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle. Commun Inf Syst 6(3): 221-251.
    • (2006) Commun Inf Syst , vol.6 , Issue.3 , pp. 221-251
    • Huang, M.1    Malhamé, R.P.2    Caines, P.E.3
  • 61
    • 34648831837 scopus 로고    scopus 로고
    • Large-population cost-coupled LQG problems with nonuniform agents: individual-mass behavior and decentralized ε{lunate}-Nash equilibria
    • Huang M, Caines PE, Malhamé RP (2007) Large-population cost-coupled LQG problems with nonuniform agents: individual-mass behavior and decentralized ε{lunate}-Nash equilibria. IEEE Trans Autom Control 52(9): 1560-1571.
    • (2007) IEEE Trans Autom Control , vol.52 , Issue.9 , pp. 1560-1571
    • Huang, M.1    Caines, P.E.2    Malhamé, R.P.3
  • 62
    • 78650003922 scopus 로고    scopus 로고
    • The NCE (mean field) principle with locality dependent cost interactions
    • Huang M, Caines P, Malhamé RP (2010) The NCE (mean field) principle with locality dependent cost interactions. IEEE Trans Autom Control 55(12): 2799-2805.
    • (2010) IEEE Trans Autom Control , vol.55 , Issue.12 , pp. 2799-2805
    • Huang, M.1    Caines, P.2    Malhamé, R.P.3
  • 64
    • 84899411582 scopus 로고    scopus 로고
    • Existence of solutions to path-dependent kinetic equations and related forward-backward systems
    • Kolokoltsov K, Yang W (2013) Existence of solutions to path-dependent kinetic equations and related forward-backward systems. Open J Optim 2: 39-44.
    • (2013) Open J Optim , vol.2 , pp. 39-44
    • Kolokoltsov, K.1    Yang, W.2
  • 65
    • 84899431120 scopus 로고    scopus 로고
    • Sensitivity analysis for HJB equations with an application to a coupled backward-forward system
    • (to appear)
    • Kolokoltsov K, Yang W (2013) Sensitivity analysis for HJB equations with an application to a coupled backward-forward system. Optimization (to appear).
    • (2013) Optimization
    • Kolokoltsov, K.1    Yang, W.2
  • 69
    • 33750627999 scopus 로고    scopus 로고
    • Jeux à champ moyen. I. Le cas stationnaire
    • Lasry J-M, Lions P-L (2006) Jeux à champ moyen. I. Le cas stationnaire. C R Math Acad Sci Paris 343(9): 619-625.
    • (2006) C R Math Acad Sci Paris , vol.343 , Issue.9 , pp. 619-625
    • Lasry, J.-M.1    Lions, P.-L.2
  • 70
    • 33751077273 scopus 로고    scopus 로고
    • Jeux à champ moyen. II. Horizon fini et contrôle optimal
    • Lasry J-M, Lions P-L (2006) Jeux à champ moyen. II. Horizon fini et contrôle optimal. C R Math Acad Sci Paris 343(10): 679-684.
    • (2006) C R Math Acad Sci Paris , vol.343 , Issue.10 , pp. 679-684
    • Lasry, J.-M.1    Lions, P.-L.2
  • 71
    • 34047127341 scopus 로고    scopus 로고
    • Mean field games
    • Lasry J-M, Lions P-L (2007) Mean field games. Jpn J Math 2(1): 229-260.
    • (2007) Jpn J Math , vol.2 , Issue.1 , pp. 229-260
    • Lasry, J.-M.1    Lions, P.-L.2
  • 76
    • 52249090671 scopus 로고    scopus 로고
    • Asymptotically optimal decentralized control for large population stochastic multiagent systems
    • Li T, Zhang J-F (2008) Asymptotically optimal decentralized control for large population stochastic multiagent systems. IEEE Trans Autom Control 53(7): 1643-1660.
    • (2008) IEEE Trans Autom Control , vol.53 , Issue.7 , pp. 1643-1660
    • Li, T.1    Zhang, J.-F.2
  • 78
    • 84892876808 scopus 로고    scopus 로고
    • IMA, University of Minessota. Video
    • Lions P-L (2012) IMA, University of Minessota. Course on mean-field games. Video, http://www. ima. umn. edu/2012-2013/sw11. 12-13. 12/.
    • (2012) Course on mean-field games
    • Lions, P.-L.1
  • 79
    • 84893935754 scopus 로고    scopus 로고
    • Knowledge growth and the allocation of time
    • Lucas RE, Moll B (2013) Knowledge growth and the allocation of time. J Polit Econ.
    • (2013) J Polit Econ
    • Lucas, R.E.1    Moll, B.2
  • 80
    • 84868369828 scopus 로고    scopus 로고
    • Linear-quadratic-Gaussian mixed games with continuum-parametrized minor players
    • Nguyen SL, Huang M (2012) Linear-quadratic-Gaussian mixed games with continuum-parametrized minor players. SIAM J Control Optim 50(5): 2907-2937.
    • (2012) SIAM J Control Optim , vol.50 , Issue.5 , pp. 2907-2937
    • Nguyen, S.L.1    Huang, M.2
  • 81
    • 84874613599 scopus 로고    scopus 로고
    • Nash, social and centralized solutions to consensus problems via mean field control theory
    • Nourian M, Caines P, Malhamé RP, Huang M (2013) Nash, social and centralized solutions to consensus problems via mean field control theory. IEEE Trans Autom Control 58(3): 639-653.
    • (2013) IEEE Trans Autom Control , vol.58 , Issue.3 , pp. 639-653
    • Nourian, M.1    Caines, P.2    Malhamé, R.P.3    Huang, M.4
  • 82
    • 84881613715 scopus 로고    scopus 로고
    • On the planning problem for the mean-field games system
    • Porretta A (2013) On the planning problem for the mean-field games system. Dyn Games Appl.
    • (2013) Dyn Games Appl
    • Porretta, A.1
  • 84
    • 84865563114 scopus 로고    scopus 로고
    • A modest proposal for MFG with density constraints
    • Santambrogio F (2012) A modest proposal for MFG with density constraints. Netw Heterog Media 7(2): 337-347.
    • (2012) Netw Heterog Media , vol.7 , Issue.2 , pp. 337-347
    • Santambrogio, F.1
  • 85
    • 0001105004 scopus 로고
    • Topics in propagation of chaos
    • Lecture notes in math, Berlin: Springer
    • Sznitman A-S (1991) Topics in propagation of chaos. In: École d'été de probabilités de Saint-Flour XIX-1989. Lecture notes in math, vol 1464. Springer, Berlin, pp 165-251.
    • (1991) École D'été De probabilités De Saint-Flour XIX-1989 , vol.1464 , pp. 165-251
    • Sznitman, A.-S.1
  • 86
    • 84962008216 scopus 로고    scopus 로고
    • Energy-constrained mean field games in wireless networks
    • (accepted)
    • Tembine H (2013) Energy-constrained mean field games in wireless networks. J Strateg Behav Environ (accepted).
    • (2013) J Strateg Behav Environ
    • Tembine, H.1
  • 88
    • 84899429640 scopus 로고    scopus 로고
    • Graduate studies in mathematics, Providence: American Mathematical Society
    • Villani C (2003) Topics in optimal transportation. Graduate studies in mathematics, vol 58. American Mathematical Society, Providence.
    • (2003) Topics in Optimal Transportation , vol.58
    • Villani, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.