EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 32 (2026) ESAIM: COCV, 32 (2026) 59 References
Open Access
Issue
ESAIM: COCV
Volume 32, 2026
Article Number 59
Number of page(s) 51
DOI https://doi.org/10.1051/cocv/2026039
Published online 14 July 2026
  1. 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) 221–252. [CrossRef] [MathSciNet] [Google Scholar]
  2. P.-L. Lasry and J.-M. Lions, Mean field games. Jpn. J. Math. 2 (2007) 229–260. [Google Scholar]
  3. P. Cardaliaguet, F. Delarue, J.-M. Lasry and P.-L. Lions, The Master Equation and the Convergence Problem in Mean Field Games (AMS-201), vol. 201. Princeton University Press (2019). [Google Scholar]
  4. R. Carmona and F. Delarue, Probabilistic Theory of Mean Field Games 'with Applications I–II. Springer (2018). [Google Scholar]
  5. D.A. Gomes, E.A. Pimentel and V. Voskanyan, Regularity Theory for Mean-Field Game Systems. Springer (2016). [Google Scholar]
  6. A. Bensoussan, J. Frehse and S.C.P. Yam, Mean Field Games and Mean Field Type Control Theory, vol. 101. Springer (2013). [Google Scholar]
  7. D. Andersson and B. Djehiche, A maximum principle for SDEs of mean-field type. Appl. Math. Optim. 63 (2011) 341–356. [Google Scholar]
  8. A. Bensoussan, P.J. Graber and S.C.P. Yam, Control on Hilbert spaces and application to some mean field type control problems. Ann. Appl. Probab. 34 (2024) 4085–4136. [Google Scholar]
  9. A. Bensoussan, K.C.J. Sung, S.C.P. Yam and S.P. Yung, Linear-quadratic mean field games. J. Optim. Theory Appl. 169 (2016) 496–529. [Google Scholar]
  10. A. Bensoussan, H.M. Tai, T.K. Wong and S.C.P. Yam, A control theoretical Approach to Mean Field Games: Part I–Global Equilibrium Solution. Appl. Math. Optim. 92 (2025) 44. [Google Scholar]
  11. A. Bensoussan, H.M. Tai, T.K. Wong, and S.C.P. Yam, A Control Theoretical Approach to Mean Field Games. Part II: Global Well-Posedness of Master Equations. Appl. Math. Optim. 93 (2026) 45. [Google Scholar]
  12. A. Bensoussan, H.M. Tai and S.C.P. Yam, Mean field type control problems, some Hilbert-space-valued fbsdes, and related equations. ESAIM Control Optim. Calc. Var. 31 (2025) 33. [Google Scholar]
  13. R. Buckdahn, B. Djehiche and J. Li, A general stochastic maximum principle for SDEs of mean-field type. Appl. Math. Optim. 64 (2011) 197–216. [Google Scholar]
  14. R. Buckdahn, J. Li and J. Ma, A mean-field stochastic control problem with partial observations. Ann. Appl. Probab. 27 (2017) 3201–3245. [Google Scholar]
  15. R. Carmona and F. Delarue, Forward–backward stochastic differential equations and controlled McKean–Vlasov dynamics. Ann. Probab. 43 (2015) 2647–2700. [CrossRef] [MathSciNet] [Google Scholar]
  16. J.-F. Chassagneux, D. Crisan and F. Delarue, A probabilistic approach to classical solutions of the master equation for large population equilibria. Mem. Am. Math. Soc. 280 (2022). [Google Scholar]
  17. A. Cosso, F. Gozzi, I. Kharroubi, H. Pham and M. Rosestolato, Optimal control of path-dependent McKean–Vlasov SDEs in infinite-dimension. Ann. Appl. Probab. 33 (2023) 2863–2918. [MathSciNet] [Google Scholar]
  18. A. Cosso and H. Pham, Zero-sum stochastic differential games of generalized McKean–Vlasov type. J. Math. Pures Appl. 129 (2019) 180–212. [Google Scholar]
  19. M.F. Djete, D. Possamaï and X. Tan, Mckean–vlasov optimal control: the dynamic programming principle. Ann. Probab. 50 (2022) 791–833. [MathSciNet] [Google Scholar]
  20. E. Pardoux and S. Peng, Backward stochastic differential equations and quasilinear parabolic partial differential equations, in Stochastic Partial Differential Equations and Their Applications. Springer (2005) 200–217. [Google Scholar]
  21. H. Pham, Linear quadratic optimal control of conditional McKean–Vlasov equation with random coefficients and applications. Probab. Uncertainty Quant. Risk 1 (2016) 1–26. [Google Scholar]
  22. H. Pham and X. Wei, Dynamic programming for optimal control of stochastic McKean–Vlasov dynamics. SIAM J. Control Optim. 55 (2017) 1069–1101. [Google Scholar]
  23. H. Pham and X. Wei, Bellman equation and viscosity solutions for mean-field stochastic control problem. ESAIM Control Optim. Calc. Var. 24 (2018) 437–461. [Google Scholar]
  24. A. Bensoussan, S.C.P. Yam and Z. Zhang, Well-posedness of mean-field type forward–backward stochastic differential equations. Stoch. Processes Appl. 125 (2015) 3327–3354. [Google Scholar]
  25. A. Bensoussan, J. Frehse and S.C.P. Yam, The master equation in mean field theory. J. Math. Pures Appl. 103 (2015) 1441–1474. [CrossRef] [MathSciNet] [Google Scholar]
  26. A. Bensoussan and S.C.P. Yam, Control problem on space of random variables and master equation. ESAIM Control Optim. Calc. Var. 25 (2019) 10. [Google Scholar]
  27. P. Cardaliaguet, M. Cirant and A. Porretta, Splitting methods and short time existence for the master equations in mean field games. J. Eur. Math. Soc. 25 (2023) 1823–1918. [Google Scholar]
  28. A. Cosso, F. Gozzi, I. Kharroubi, H. Pham and M. Rosestolato, Master Bellman equation in the Wasserstein space: Uniqueness of viscosity solutions. Trans. Am. Math. Soc. (2023). [Google Scholar]
  29. W. Gangbo and A. R. Mészáros, Global well-posedness of master equations for deterministic displacement convex potential mean field games. Commun. Pure Appl. Math. 75 (2022) 2685–2801. [Google Scholar]
  30. W. Gangbo, A. R Mészáros, C. Mou and J. Zhang, Mean field games master equations with nonseparable Hamiltonians and displacement monotonicity. Ann. Probab. 50 (2022) 2178–2217. [CrossRef] [MathSciNet] [Google Scholar]
  31. W. Gangbo and A. Święch, Existence of a solution to an equation arising from the theory of mean field games. J. Differ. Equ. 259 (2015) 6573–6643. [Google Scholar]
  32. M. Laurière and O. Pironneau, Dynamic programming for mean-field type control. Comptes Rendus Math. 352 (2014) 707–713. [Google Scholar]
  33. J. Li, Stochastic maximum principle in the mean-field controls. Automatica 48 (2012) 366–373. [Google Scholar]
  34. R. Carmona, F. Delarue and A. Lachapelle, Control of McKean–Vlasov dynamics versus mean field games. Math. Financial Econ. 7 (2013) 131–166. [Google Scholar]
  35. J. Yong, Linear-quadratic optimal control problems for mean-field stochastic differential equations. SIAM J. Control Optim. 51 (2013) 2809–2838. [Google Scholar]
  36. P. Cardaliaguet, Weak solutions for first order mean field games with local coupling. Analysis and Geometry in Control Theory and its Applications (2015) 111–158. [Google Scholar]
  37. P.J. Graber, Optimal control of first-order Hamilton–Jacobi equations with linearly bounded Hamiltonian. Appl. Math. Optim. 70 (2014) 185–224. [Google Scholar]
  38. P. Cardaliaguet and P.J. Graber, Mean field games systems of first order. ESAIM Control Optim. Calc. Var. 21 (2015) 690–722. [MathSciNet] [Google Scholar]
  39. A. Porretta, Weak solutions to Fokker–Planck equations and mean field games. Arch. Rational Mech. Anal. 216 (2015) 1–62. [Google Scholar]
  40. D. Ambrose, Strong solutions for time-dependent mean field games with non-separable Hamiltonians. J. Math. Pures Appl. 113 (2018) 141–154. [Google Scholar]
  41. P.-L. Lions, Cours au Collège de France. [Google Scholar]
  42. P. Cardaliaguet, Notes on mean-field games (from P.-L. Lions' lectures at College de France) (2013). [Google Scholar]
  43. A. Bensoussan, J. Frehse and S.C.P. Yam, On the interpretation of the master equation. Stoch. Processes Appl. 127 (2017) 2093–2137. [Google Scholar]
  44. S. Mayorga, Short time solution to the master equation of a first order mean field game. J. Differ. Equ. 268 (2020) 6251–6318. [Google Scholar]
  45. D. Ambrose and A. Mészáros, Well-posedness of mean field games master equations involving non-separable local Hamiltonians. Trans. Am. Math. Soc. 376 (2023) 2481–2523. [Google Scholar]
  46. C. Mou and J. Zhang, Wellposedness of second order master equations for mean field games with nonsmooth data. Mem. Am. Math. Soc. (2021). [Google Scholar]
  47. C. Bertucci, Monotone solutions for mean field games master equations: continuous state space and common noise. Commun. Part. Differ. Equ. 48 (2023) 1245–1285. [Google Scholar]
  48. P. Cardaliaguet and P. Souganidis, Monotone Solutions of the Master Equation for Mean Field Games with Idiosyncratic Noise. SIAM J. Math. Anal. 54 (2022). DOI: https://doi.org/10.1137/21M1450008 [Google Scholar]
  49. A. Cecchin, D.P. Paolo, F. Markus and P. Guglielmo, On the convergence problem in mean field games: a two state model without uniqueness. SIAM J. Control Optim. 57 (2019) 2443–2466. [Google Scholar]
  50. F. Delarue and R.F. Tchuendom, Selection of equilibria in a linear quadratic mean-field game. Stoch. Processes Appl. 130 (2020) 1000–1040. [Google Scholar]
  51. S. Ahuja, Wellposedness of mean field games with common noise under a weak monotonicity condition. SIAM J. Control Optim. 54 (2016) 30–48. [Google Scholar]
  52. A. Bensoussan, T.K. Wong, S.C.P. Yam and H. Yuan, A theory of first order mean field type control problems and their equations. J. Eur. Math. Soc. (2026), published online first. DOI: https://doi.org/10.4171/JEMS/1781 [Google Scholar]
  53. P.J. Graber and A.R. Mészáros, On monotonicity conditions for mean field games. J. Funct. Anal. 285 (2023) 110095. [Google Scholar]
  54. A. Bensoussan, Z. Huang, S. Tang, and S.C.P. Yam, On mean field monotonicity conditions from a control theoretical perspective. Rend. Lincei Mat. Appl. 36 (2025) 89–137. [Google Scholar]
  55. A. Cecchin and F. Delarue Weak solutions to the Master Equation of Potential Mean Field Games. Mem. Am. Math. Soc. (2025). DOI: https://doi.org/10.1090/memo/1600 [Google Scholar]
  56. P.J. Graber and A. Mészáros, On some mean field games and master equations through the lens of conservation laws. Math. Ann. 390 (2024) 4497–4533. [Google Scholar]
  57. P.-L. Lions and P.E. Souganidis, Homogenization of the backward–forward mean-field games systems in periodic environments. Rend. Lincei 31 (2021) 733–755. [Google Scholar]
  58. J.-M. Lasry, P.-L. Lions and B. Seeger, Dimension reduction techniques in deterministic mean field games. Commun. Part. Differ. Equ. 47 (2022) 701–723. [Google Scholar]
  59. R. Carmona and D. Lacker, A probabilistic weak formulation of mean field games and applications. The Ann. Appl. Probab. 25 (2018) 1189–1231. [Google Scholar]
  60. R. Carmona, F. Delarue and D. Lacker, Mean field games with common noise. Ann. Probab. 44 (2016) 3740–3803. [MathSciNet] [Google Scholar]
  61. R. Buckdahn, J. Li, S. Peng and C. Rainer, Mean-field stochastic differential equations and associated PDEs. Ann. Probab. 45 (2017) 824–878. [CrossRef] [MathSciNet] [Google Scholar]
  62. R. Buckdahn, B. Djehiche, J. Li and S. Peng, Mean-field backward stochastic differential equations: a limit approach. Ann. Probab. 37 (2009) 1524–1565. [Google Scholar]
  63. R. Buckdahn, J. Li and S. Peng, Mean-field backward stochastic differential equations and related partial differential equations. Stoch. Processes Appl. 119 (2009) 3133–3154. [Google Scholar]
  64. R. Carmona and F. Delarue. Mean field forward–backward stochastic differential equations. Electron. Commun. Probab. 18 (2013) 1–15. [CrossRef] [MathSciNet] [Google Scholar]
  65. L. Ambrosio, N. Gigli and G. Savare, Gradient Flows: In Metric Spaces and in the Space of Probability Measures. Springer Science & Business Media (2008). [Google Scholar]
  66. M. Bansil and A. Mészáros, Hidden monotonicity and canonical transformations for mean field games and master equations, in Forum of Mathematics, Sigma, vol. 13. Cambridge University Press (2025) e182. [Google Scholar]
  67. M. Bansil, A. Mészáros and C. Mou, Global well-posedness of displacement monotone degenerate mean field games master equations. SIAM J. Control Optim. 63 (2025) 993–1021. [Google Scholar]
  68. P. Caines, Mean field game control theory: Introduction and recent results. https://www.cityu.edu.hk/ma/news-events/mean-field-game-control-theory-introduction-and-recent-results (2015). [Google Scholar]
  69. A. Bensoussan, Estimation and Control of Dynamical Systems, vol. 48. Springer (2018). [Google Scholar]
  70. C. Bertucci, J.-M. Lasry and P.-L. Lions, On Lipschitz solutions of mean field games master equations. J. Funct. Anal. 287 (2024) 110486. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.