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Volumn 148, Issue 10, 2020, Pages 4241-4255

Remarks on nash equilibria in mean field game models with a major player

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EID: 85096132136     PISSN: 00029939     EISSN: 10886826     Source Type: Journal    
DOI: 10.1090/proc/15135     Document Type: Article
Times cited : (29)

References (26)
  • 2
    • 84940646547 scopus 로고    scopus 로고
    • Mean field Stackelberg games: aggregation of delayed instructions
    • MR3376121
    • A. Bensoussan, M. H. M. Chau, and S. C. P. Yam, Mean field Stackelberg games: aggregation of delayed instructions, SIAM J. Control Optim. 53 (2015), no. 4, 2237–2266, DOI 10.1137/140993399. MR3376121
    • (2015) SIAM J. Control Optim , vol.53 , Issue.4 , pp. 2237-2266
    • Bensoussan, A.1    Chau, M. H. M.2    Yam, S. C. P.3
  • 3
    • 84937898078 scopus 로고    scopus 로고
    • Mean field games with a dominating player
    • A. Bensoussan, M. H. M. Chau, and S. C. P. Yam, Appl. Math. Optim, 10.1007/s00245-015-9309-1, MR3518868 [4] Rainer Buckdahn, Juan Li, and Nonlinear stochastic differential games involving a major player and a larg of collectively acting minor agents, 52 (2014) 1, 451–492, MR3163233
    • A. Bensoussan, M. H. M. Chau, and S. C. P. Yam, Mean field games with a dominating player, Appl. Math. Optim. 74 (2016), no. 1, 91–128, DOI 10.1007/s00245-015-9309-1. MR3518868 [4] Rainer Buckdahn, Juan Li, and Shige Peng, Nonlinear stochastic differential games involving a major player and a large number of collectively acting minor agents, SIAM J. Control Optim. 52 (2014), no. 1, 451–492, DOI 10.1137/130933174. MR3163233
    • (2016) SIAM J. Control Optim , vol.74 , Issue.1 , pp. 91-128
    • Peng, Shige1
  • 4
    • 84929727652 scopus 로고    scopus 로고
    • Mean field estimation for partially observed LQG systems with major and minor agents
    • P. E. Caines and A. C. Kizilkale, Mean field estimation for partially observed LQG systems with major and minor agents, IFAC Proceedings Volumes, 47(3), 2014, pp. 8705-8709.
    • (2014) IFAC Proceedings Volumes , vol.47 , Issue.3 , pp. 8705-8709
    • Caines, P. E.1    Kizilkale, A. C.2
  • 9
    • 85021722713 scopus 로고    scopus 로고
    • An alternative approach to mean field game with major and minor players, and applications to herders impacts
    • MR3679337
    • Rene Carmona and Peiqi Wang, An alternative approach to mean field game with major and minor players, and applications to herders impacts, Appl. Math. Optim. 76 (2017), no. 1, 5–27, DOI 10.1007/s00245-017-9430-4. MR3679337
    • (2017) Appl. Math. Optim , vol.76 , Issue.1 , pp. 5-27
    • Carmona, Rene1    Wang, Peiqi2
  • 10
    • 84979084054 scopus 로고    scopus 로고
    • A probabilistic approach to mean field games with major and minor players
    • MR3513598
    • René Carmona and Xiuneng Zhu, A probabilistic approach to mean field games with major and minor players, Ann. Appl. Probab. 26 (2016), no. 3, 1535–1580, DOI 10.1214/15-AAP1125. MR3513598
    • (2016) Ann. Appl. Probab , vol.26 , Issue.3 , pp. 1535-1580
    • Carmona, René1    Zhu, Xiuneng2
  • 12
    • 85068572470 scopus 로고    scopus 로고
    • A tale of a principal and many, many agents
    • MR3959080
    • Romuald Elie, Thibaut Mastrolia, and Dylan Possamaï, A tale of a principal and many, many agents, Math. Oper. Res. 44 (2019), no. 2, 440–467, DOI 10.1287/moor.2018.0931. MR3959080
    • (2019) Math. Oper. Res , vol.44 , Issue.2 , pp. 440-467
    • Elie, Romuald1    Mastrolia, Thibaut2    Possamaï, Dylan3
  • 13
    • 84962010106 scopus 로고    scopus 로고
    • Nash equilibria for partially observed LQG mean field games with major agent: Partial observations by all agents, Decision and Control (CDC)
    • D. Firoozi and P. E. Caines, Nash equilibria for partially observed LQG mean field games with major agent: Partial observations by all agents, Decision and Control (CDC), 2015 IEEE 54th Annual Conference, pp. 4430–4437.
    • 2015 IEEE 54th Annual Conference , pp. 4430-4437
    • Firoozi, D.1    Caines, P. E.2
  • 14
    • 0039930261 scopus 로고
    • Stochastic differential games
    • MR292528
    • Avner Friedman, Stochastic differential games, J. Differential Equations 11 (1972), 79–108, DOI 10.1016/0022-0396(72)90082-4. MR292528
    • (1972) J. Differential Equations , vol.11 , pp. 79-108
    • Friedman, Avner1
  • 15
    • 84941797484 scopus 로고    scopus 로고
    • Existence of a solution to an equation arising from the theory of mean field games
    • MR3397332
    • Wilfrid Gangbo and Andrzej Swie ´ ch, Existence of a solution to an equation arising from the theory of mean field games, J. Differential Equations 259 (2015), no. 11, 6573–6643, DOI 10.1016/j.jde.2015.08.001. MR3397332
    • (2015) J. Differential Equations , vol.259 , Issue.11 , pp. 6573-6643
    • Gangbo, Wilfrid1    Swie ´ ch, Andrzej2
  • 16
    • 79952140932 scopus 로고    scopus 로고
    • Large-population LQG games involving a major player: the Nash certainty equivalence principle
    • (/10) MR2599921
    • Minyi Huang, Large-population LQG games involving a major player: the Nash certainty equivalence principle, SIAM J. Control Optim. 48 (2009/10), no. 5, 3318–3353, DOI 10.1137/080735370. MR2599921
    • (2009) SIAM J. Control Optim , vol.48 , Issue.5 , pp. 3318-3353
    • Huang, Minyi1
  • 17
    • 84930627228 scopus 로고    scopus 로고
    • LQ Nash games with random entrance: an infinite horizon major player and minor players of finite horizons
    • MR3353388
    • Ioannis Kordonis and George P. Papavassilopoulos, LQ Nash games with random entrance: an infinite horizon major player and minor players of finite horizons, IEEE Trans. Automat. Control 60 (2015), no. 6, 1486–1500, DOI 10.1109/TAC.2015.2396642. MR3353388
    • (2015) IEEE Trans. Automat. Control , vol.60 , Issue.6 , pp. 1486-1500
    • Kordonis, Ioannis1    Papavassilopoulos, George P.2
  • 18
    • 33750627999 scopus 로고    scopus 로고
    • Jeux à champ moyen. I. Le cas stationnaire (French, with English and French summaries)
    • MR2269875
    • Jean-Michel Lasry and Pierre-Louis Lions, Jeux à champ moyen. I. Le cas stationnaire (French, with English and French summaries), C. R. Math. Acad. Sci. Paris 343 (2006), no. 9, 619–625, DOI 10.1016/j.crma.2006.09.019. MR2269875
    • (2006) C. R. Math. Acad. Sci. Paris , vol.343 , Issue.9 , pp. 619-625
    • Lasry, Jean-Michel1    Lions, Pierre-Louis2
  • 19
    • 33751077273 scopus 로고    scopus 로고
    • Jeux à champ moyen. II. Horizon fini et contrôle optimal (French, with English and French summaries)
    • MR2271747
    • Jean-Michel Lasry and Pierre-Louis Lions, Jeux à champ moyen. II. Horizon fini et contrôle optimal (French, with English and French summaries), C. R. Math. Acad. Sci. Paris 343 (2006), no. 10, 679–684, DOI 10.1016/j.crma.2006.09.018. MR2271747
    • (2006) C. R. Math. Acad. Sci. Paris , vol.343 , Issue.10 , pp. 679-684
    • Lasry, Jean-Michel1    Lions, Pierre-Louis2
  • 20
    • 34047127341 scopus 로고    scopus 로고
    • Mean field games
    • MR2295621
    • Jean-Michel Lasry and Pierre-Louis Lions, Mean field games, Jpn. J. Math. 2 (2007), no. 1, 229–260, DOI 10.1007/s11537-007-0657-8. MR2295621
    • (2007) Jpn. J. Math , vol.2 , Issue.1 , pp. 229-260
    • Lasry, Jean-Michel1    Lions, Pierre-Louis2
  • 21
    • 85048748466 scopus 로고    scopus 로고
    • Mean-field games with a major player (English, with English and French summaries)
    • MR3851543
    • Jean-Michel Lasry and Pierre-Louis Lions, Mean-field games with a major player (English, with English and French summaries), C. R. Math. Acad. Sci. Paris 356 (2018), no. 8, 886–890, DOI 10.1016/j.crma.2018.06.001. MR3851543
    • (2018) C. R. Math. Acad. Sci. Paris , vol.356 , Issue.8 , pp. 886-890
    • Lasry, Jean-Michel1    Lions, Pierre-Louis2
  • 23
    • 84962019957 scopus 로고    scopus 로고
    • Linear-quadratic stochastic differential Stackelberg games with a high population of followers, Decision and Control (CDC)
    • J. Moon and T. Başar, Linear-quadratic stochastic differential Stackelberg games with a high population of followers, Decision and Control (CDC), 2015 IEEE 54th Annual Conference, pp. 2270–2275.
    • 2015 IEEE 54th Annual Conference , pp. 2270-2275
    • Moon, J.1    Başar, T.2
  • 24
    • 84874257088 scopus 로고    scopus 로고
    • Mean field LQG games with mass behavior responsive to a major player, Decision and Control (CDC)
    • S. L. Nguyen and M. Huang, Mean field LQG games with mass behavior responsive to a major player, Decision and Control (CDC), 2012 IEEE 51st Annual Conference, pp. 5792–5797.
    • 2012 IEEE 51st Annual Conference , pp. 5792-5797
    • Nguyen, S. L.1    Huang, M.2
  • 25
    • 84888865707 scopus 로고    scopus 로고
    • Nash mean field game theory for nonlinear stochastic dynamical systems with major and minor agents
    • MR3092738
    • Mojtaba Nourian and Peter E. Caines, Nash mean field game theory for nonlinear stochastic dynamical systems with major and minor agents, SIAM J. Control Optim. 51 (2013), no. 4, 3302–3331, DOI 10.1137/120889496. MR3092738
    • (2013) SIAM J. Control Optim , vol.51 , Issue.4 , pp. 3302-3331
    • Nourian, Mojtaba1    Caines, Peter E.2
  • 26
    • 85096102755 scopus 로고    scopus 로고
    • Mass transportation problems. Vol. II, Probability and its Applications (New York), Springer-Verlag, New York, 1998
    • Applications. MR1619171 [28] Nevroz Şen and Peter E. Caines, Mean field game theory with a partially observed major agent, SIAM J. Control Optim. 54 (2016) 6, –3224, MR3579694 [29] Cédric Villani, Optimal transport, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 338, Springer-Verlag, Berlin, 2009. Old and new. MR2459454
    • Svetlozar T. Rachev and Ludger Rüschendorf, Mass transportation problems. Vol. II, Probability and its Applications (New York), Springer-Verlag, New York, 1998. Applications. MR1619171 [28] Nevroz Şen and Peter E. Caines, Mean field game theory with a partially observed major agent, SIAM J. Control Optim. 54 (2016), no. 6, 3174–3224, DOI 10.1137/16M1063010. MR3579694 [29] Cédric Villani, Optimal transport, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 338, Springer-Verlag, Berlin, 2009. Old and new. MR2459454
    • Rachev, Svetlozar T.1    Rüschendorf, Ludger2


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