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Volumn 125, Issue 7, 2015, Pages 2856-2894

Mean field games via controlled martingale problems: Existence of Markovian equilibria

Author keywords

Controlled martingale problem; Mean field games; Relaxed control

Indexed keywords

STATISTICS;

EID: 84933553528     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2015.02.006     Document Type: Article
Times cited : (145)

References (43)
  • 1
  • 6
    • 0026867786 scopus 로고
    • Stochastic differential games: Occupation measure based approach
    • V.S. Borkar, and M.K. Ghosh Stochastic differential games: occupation measure based approach J. Optim. Theory Appl. 73 2 1992 359 385
    • (1992) J. Optim. Theory Appl. , vol.73 , Issue.2 , pp. 359-385
    • Borkar, V.S.1    Ghosh, M.K.2
  • 7
    • 84879748254 scopus 로고    scopus 로고
    • Mimicking an Itô process by a solution of a stochastic differential equation
    • G. Brunick, and S. Shreve Mimicking an Itô process by a solution of a stochastic differential equation Ann. Appl. Probab. 23 4 2013 1584 1628
    • (2013) Ann. Appl. Probab. , vol.23 , Issue.4 , pp. 1584-1628
    • Brunick, G.1    Shreve, S.2
  • 13
    • 84876129326 scopus 로고    scopus 로고
    • Control of McKean-Vlasov dynamics versus mean field games
    • R. Carmona, F. Delarue, and A. Lachapelle Control of McKean-Vlasov dynamics versus mean field games Math. Financ. Econ. 7 2 2013 131 166
    • (2013) Math. Financ. Econ. , vol.7 , Issue.2 , pp. 131-166
    • Carmona, R.1    Delarue, F.2    Lachapelle, A.3
  • 16
    • 84939992159 scopus 로고    scopus 로고
    • A probabilistic weak formulation of mean field games and applications
    • appeared online
    • R. Carmona, and D. Lacker A probabilistic weak formulation of mean field games and applications Ann. Appl. Probab. 2014 appeared online
    • (2014) Ann. Appl. Probab.
    • Carmona, R.1    Lacker, D.2
  • 17
    • 84855914238 scopus 로고    scopus 로고
    • On the existence of strict optimal controls for constrained, controlled Markov processes in continuous time
    • F. Dufour, and R.H. Stockbridge On the existence of strict optimal controls for constrained, controlled Markov processes in continuous time Stochastics 84 1 2012 55 78
    • (2012) Stochastics , vol.84 , Issue.1 , pp. 55-78
    • Dufour, F.1    Stockbridge, R.H.2
  • 19
    • 0001274938 scopus 로고
    • Compactification methods in the control of degenerate diffusions: Existence of an optimal control
    • N. El Karoui, D.H. Nguyen, and M. Jeanblanc-Picqué Compactification methods in the control of degenerate diffusions: existence of an optimal control Stochastics 20 3 1987 169 219
    • (1987) Stochastics , vol.20 , Issue.3 , pp. 169-219
    • El Karoui, N.1    Nguyen, D.H.2    Jeanblanc-Picqué, M.3
  • 20
    • 85086705967 scopus 로고
    • Fixed-point and minimax theorems in locally convex topological linear spaces
    • K. Fan Fixed-point and minimax theorems in locally convex topological linear spaces Proc. Natl. Acad. Sci. USA 38 2 1952 121
    • (1952) Proc. Natl. Acad. Sci. USA , vol.38 , Issue.2 , pp. 121
    • Fan, K.1
  • 21
    • 0002764036 scopus 로고
    • On certain questions in the theory of optimal control
    • A.F. Filippov On certain questions in the theory of optimal control J. Soc. Ind. Appl. Math., Ser. A: Control 1 1 1962 76 84
    • (1962) J. Soc. Ind. Appl. Math., Ser. A: Control , vol.1 , Issue.1 , pp. 76-84
    • Filippov, A.F.1
  • 25
    • 84973259353 scopus 로고    scopus 로고
    • Mean field games models - A brief survey
    • D.A. Gomes, and J. Saúde Mean field games models - a brief survey Dyn. Games Appl. 2013 1 45
    • (2013) Dyn. Games Appl. , pp. 1-45
    • Gomes, D.A.1    Saúde, J.2
  • 26
    • 77958476920 scopus 로고    scopus 로고
    • Mean field games and applications
    • Lecture Notes in Mathematics Springer Berlin, Heidelberg
    • O. Guéant, J.M. Lasry, and P.L. Lions Mean field games and applications Paris-Princeton Lectures on Mathematical Finance 2010 Lecture Notes in Mathematics vol. 2003 2011 Springer Berlin, Heidelberg 205 266
    • (2011) Paris-Princeton Lectures on Mathematical Finance 2010 , vol.2003 VOL. , pp. 205-266
    • Guéant, O.1    Lasry, J.M.2    Lions, P.L.3
  • 27
    • 0000335830 scopus 로고
    • Mimicking the one-dimensional marginal distributions of processes having an Itô differential
    • I. Gyöngy Mimicking the one-dimensional marginal distributions of processes having an Itô differential Probab. Theory Related Fields 71 4 1986 501 516
    • (1986) Probab. Theory Related Fields , vol.71 , Issue.4 , pp. 501-516
    • Gyöngy, I.1
  • 29
    • 79952140932 scopus 로고    scopus 로고
    • Large-population LQG games involving a major player: The Nash certainty equivalence principle
    • M. Huang Large-population LQG games involving a major player: the Nash certainty equivalence principle SIAM J. Control Optim. 48 5 2010 3318 3353
    • (2010) SIAM J. Control Optim. , vol.48 , Issue.5 , pp. 3318-3353
    • Huang, M.1
  • 30
    • 39549087376 scopus 로고    scopus 로고
    • Large population stochastic dynamic games: Closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle
    • M. Huang, R. Malhamé, and P. Caines Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle Commun. Inf. Syst. 6 3 2006 221 252
    • (2006) Commun. Inf. Syst. , vol.6 , Issue.3 , pp. 221-252
    • Huang, M.1    Malhamé, R.2    Caines, P.3
  • 31
    • 0000555789 scopus 로고
    • Sur un type de convergence intermédiaire entre la convergence en loi et la convergence en probabilité
    • J. Jacod, and J. Mémin Sur un type de convergence intermédiaire entre la convergence en loi et la convergence en probabilité Sém. Probab. Strasbg. 15 1981 529 546
    • (1981) Sém. Probab. Strasbg. , vol.15 , pp. 529-546
    • Jacod, J.1    Mémin, J.2
  • 33
    • 0032024929 scopus 로고    scopus 로고
    • Existence of Markov controls and characterization of optimal Markov controls
    • T.G. Kurtz, and R.H. Stockbridge Existence of Markov controls and characterization of optimal Markov controls SIAM J. Control Optim. 36 2 1998 609 653
    • (1998) SIAM J. Control Optim. , vol.36 , Issue.2 , pp. 609-653
    • Kurtz, T.G.1    Stockbridge, R.H.2
  • 35
    • 33750627999 scopus 로고    scopus 로고
    • Jeux à champ moyen. I-Le cas stationnaire
    • J.M. Lasry, and P.L. Lions Jeux à champ moyen. I-Le cas stationnaire C. R. Math. 343 9 2006 619 625
    • (2006) C. R. Math. , vol.343 , Issue.9 , pp. 619-625
    • Lasry, J.M.1    Lions, P.L.2
  • 36
    • 33751077273 scopus 로고    scopus 로고
    • Jeux à champ moyen. II-Horizon fini et contrôle optimal
    • J.M. Lasry, and P.L. Lions Jeux à champ moyen. II-Horizon fini et contrôle optimal C. R. Math. 343 10 2006 679 684
    • (2006) C. R. Math. , vol.343 , Issue.10 , pp. 679-684
    • Lasry, J.M.1    Lions, P.L.2
  • 38
    • 0002021736 scopus 로고
    • Equilibrium points in n-person games
    • J. Nash Equilibrium points in n-person games Proc. Natl. Acad. Sci. 36 1 1950 48 49
    • (1950) Proc. Natl. Acad. Sci. , vol.36 , Issue.1 , pp. 48-49
    • Nash, J.1
  • 39
    • 0000843831 scopus 로고
    • Relations between weak and uniform convergence of measures with applications
    • R. Rao Relations between weak and uniform convergence of measures with applications Ann. Math. Statist. 1962 659 680
    • (1962) Ann. Math. Statist. , pp. 659-680
    • Rao, R.1
  • 41
    • 0001105004 scopus 로고
    • Topics in propagation of chaos
    • Lecture Notes in Mathematics Springer Berlin, Heidelberg
    • A.S. Sznitman Topics in propagation of chaos Ecole d'eté de Probabilités de Saint-Flour XIX - 1989 Lecture Notes in Mathematics vol. 1464 1991 Springer Berlin, Heidelberg 165 251
    • (1991) Ecole d'Eté de Probabilités de Saint-Flour XIX - 1989 , vol.1464 VOL. , pp. 165-251
    • Sznitman, A.S.1
  • 42
    • 2442557820 scopus 로고    scopus 로고
    • Graduate Studies in Mathematics American Mathematical Society
    • C. Villani Topics in Optimal Transportation Graduate Studies in Mathematics 2003 American Mathematical Society
    • (2003) Topics in Optimal Transportation
    • Villani, C.1


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