Open Access
Issue
ESAIM: COCV
Volume 29, 2023
Article Number 39
Number of page(s) 42
DOI https://doi.org/10.1051/cocv/2023005
Published online 09 June 2023
  1. C. Alasseur, I. Ben Taher and A. Matoussi, An extended mean field game for storage in smart grids. J. Optim. Theory Applic. 184 (2020) 644–670. [CrossRef] [Google Scholar]
  2. D.G. Aronson and J. Serrin, Local behavior of solutions of quasilinear parabolic equations. Vol. 25 of Archive for Rational Mechanics and Analysis (1967) 81–122. [CrossRef] [MathSciNet] [Google Scholar]
  3. E. Bayraktar, A. Cecchin, A. Cohen and F. Delarue, Finite state mean field games with wright–fisher common noise. J. Math. Pures Appl. 147 (2021) 98–162. [CrossRef] [MathSciNet] [Google Scholar]
  4. A. Bensoussan and S.C.P. Yam, Control problem on space of random variables and master equation. ESAIM: COCV 25 (2019) 10. [CrossRef] [EDP Sciences] [Google Scholar]
  5. C. Bertucci, Monotone solutions for mean field games master equations : finite state space and optimal stopping. arXiv preprint arXiv:2007.11854, 2021. [Google Scholar]
  6. C. Bertucci, Monotone solutions for mean field games master equations : continuous state space and common noise. arXiv preprint arXiv:2107.09531, 2021. [Google Scholar]
  7. V.I. Bogachev, N.V. Krylov, M. Röckner and S.V. Shaposhnikov, Fokker–Planck–Kolmogorov Equations. Mathematical Surveys and Monographs. American Mathematical Society (2015). [CrossRef] [Google Scholar]
  8. J.F. Bonnans, S. Hadikhanloo and L. Pfeiffer, Schauder estimates for a class of potential mean field games of controls. Appl. Math. Optim. 83 (2019) 1431–1464. [Google Scholar]
  9. P. Cardaliaguet, Notes on mean field games (from P.-L. Lions’ lectures at Collège de France). Lecture given at Tor Vergata, April–May 2010 (2010). [Google Scholar]
  10. P. Cardaliaguet and C.-A. Lehalle, Mean field game of controls and an application to trade crowding. Math. Finan. Econ. 12 (2018) 335–363. [CrossRef] [Google Scholar]
  11. P. Cardaliaguet and C. Rainer, An example of multiple mean field limits in ergodic differential games. Nonlinear Diff. Equ. Applic. NoDEA 27 (2020). [Google Scholar]
  12. P. Cardaliaguet, F. Delarue, J.-M. Lasry and P.-L. Lions, The Master Equation and the Convergence Problem in Mean Field Games. Vol. 201 of Annals of Mathematics Studies. Princeton University Press (2019). [Google Scholar]
  13. R. Carmona and F. Delarue, Probabilistic Theory of Mean Field Games with Applications I. Vol. 83 of Probability Theory and Stochastic Modelling. Springer International Publishing (2018). [Google Scholar]
  14. R. Carmona and F. Delarue, Probabilistic Theory of Mean Field Games with Applications II. Vol. 84 of Probability Theory and Stochastic Modelling. Springer International Publishing (2018). [Google Scholar]
  15. R. Carmona and D. Lacker, A probabilistic weak formulation of mean field games and applications. Ann. Appl. Probab. 25 (2015) 1189–1231. [CrossRef] [MathSciNet] [Google Scholar]
  16. R. Carmona, F. Delarue and D. Lacker, Mean field games with common noise. Ann. Probab. 44 (2016) 3740–3803. [MathSciNet] [Google Scholar]
  17. C. Castaing, P. Raynaud de Fitte and M. Valadier, Young Measures on Topological Spaces With Applications in Control Theory and Probability Theory/by Charles Castaing, Paul Raynaud de Fitte, Michel Valadier. Mathematics and Its Applications, 1st ed. Vol. 571. Springer Netherlands: Imprint: Springer, Dordrecht (2004). [Google Scholar]
  18. S. Cobzas, R. Miculescu and A. Nicolae, Approximations Involving Lipschitz Functions. Springer International Publishing, Cham (2019), 317–334. [CrossRef] [Google Scholar]
  19. F. Delarue, Restoring uniqueness to mean-field games by randomizing the equilibria. Stochast. Partial Diff. Equ. Anal. Comput. 7 (2019) 598–678. [Google Scholar]
  20. F. Delarue and A. Vasileiadis, Exploration noise for learning linear-quadratic mean field games. arXiv preprint arXiv:2107.00839, 2021. [CrossRef] [Google Scholar]
  21. F. Delarue, D. Lacker and K. Ramanan, From the master equation to mean field game limit theory: a central limit theorem. Electron. J. Probab. 24 (2019) 1–54. [CrossRef] [Google Scholar]
  22. F. Delarue, D. Lacker and K. Ramanan, From the master equation to mean field game limit theory: Large deviations and concentration of measure. Ann. Probab. 48 (2020) 211–263. [CrossRef] [MathSciNet] [Google Scholar]
  23. M.F. Djete, Mean field games of controls: on the convergence of Nash equilibria. arXiv Preprint arXiv:2006.12993, 2020. [Google Scholar]
  24. M.F. Djete, Some Results on the McKean–Vlasov Optimal Control and Mean Field Games: Limit Theorems, Dynamic Programming Principle and Numerical Approximations. PhD thesis, Université Paris Dauphine PSL, 2020. [Google Scholar]
  25. M.F. Djete, Extended mean field control problem: a propagation of chaos result. Electron. J. Probab. 27 (2022) 1–53. [CrossRef] [Google Scholar]
  26. M.F. Djete, D. Possamaï and X. Tan, Mckean–vlasov optimal control: limit theory and equivalence between different formulations. Math. Oper. Res. [Google Scholar]
  27. N. El Karoui, D. Huu Nguyen and M. Jeanblanc-Picqué, Compactification methods in the control of degenerate diffusions: existence of an optimal control. Stochastics 20 (1987) 169–219. [CrossRef] [MathSciNet] [Google Scholar]
  28. A.F. Filippov, On certain questions in the theory of optimal control. J. Soc. Ind. Appl. Math. A Control 1 (1962) 76–84. [CrossRef] [Google Scholar]
  29. M. Fisher, On the connection between symmetric n-player games and mean field games. Ann. Appl. Probab. 27 (2017) 757–810. [MathSciNet] [Google Scholar]
  30. W. Gangbo and A. Świech, Existence of a solution to an equation arising from the theory of mean field games. J. Diff. Equ. 259 (2015) 6573–6643. [CrossRef] [Google Scholar]
  31. D.A. Gomes and V.K. Voskanyan, Extended deterministic mean-field games. SIAM J. Control Optim. 54 (2016) 1030–1055. [CrossRef] [MathSciNet] [Google Scholar]
  32. D.A. Gomes, S. Patrizi and V. Voskanyan, On the existence of classical solutions for stationary extended mean field games. Nonlinear Anal. Theory Methods Applic. 99 (2014) 49–79. [CrossRef] [Google Scholar]
  33. P.J. Graber, Linear quadratic mean field type control and mean field games with common noise, with application to production of an exhaustible resource. Appl. Math. Optim. 74 (2016) 459–486. [CrossRef] [MathSciNet] [Google Scholar]
  34. M. Huang, P. Caines and R. Malhamé, Individual and mass behaviour in large population stochastic wireless power control problems: centralized and Nash equilibrium solutions, in C. Abdallah and F. Lewis, editors, Proceedings of the 42nd IEEE Conference on Decision and Control, 2003. IEEE (2003), 98–103. [Google Scholar]
  35. M. Huang, R. Malhamé and P. Caines, Large population stochastic dynamic games: closed–loop McKean–Vlasov systems and the Nash certainty equivalence principle. Commun. Inform. Syst. 6 (2006) 221–252. [CrossRef] [Google Scholar]
  36. Z. Kobeissi, On classical solutions to the mean field game system of controls. arXiv preprint arXiv:1904.11292, 2019. [Google Scholar]
  37. T.G. Kurtz and J. Xiong, Particle representations for a class of nonlinear spdes. Stoch. Processes Applic. 83 (1999) 103–126. [CrossRef] [Google Scholar]
  38. D. Lacker, A general characterization of the mean field limit for stochastic differential games. Probab. Theory Related Fields 165 (2016) 581–648. [CrossRef] [MathSciNet] [Google Scholar]
  39. D. Lacker, Limit theory for controlled McKean–Vlasov dynamics. SIAM J. Control Optim. 55 (2017) 1641–1672. [CrossRef] [MathSciNet] [Google Scholar]
  40. D. Lacker, On a strong form of propagation of chaos for McKean-Vlasov equations. Electron. Commun. Probab. 23 (2018) 1–11. [CrossRef] [MathSciNet] [Google Scholar]
  41. D. Lacker, On the convergence of closed-loop Nash equilibria to the mean field game limit. Ann. Appl. Probab. 30 (2020) 1693–1761. [CrossRef] [MathSciNet] [Google Scholar]
  42. D. Lacker and L.L. Flem, Closed-loop convergence for mean field games with common noise. arXiv preprint arXiv:2107.03273, 2021. [Google Scholar]
  43. D. Lacker, M. Shkolnikov and J. Zhang, Superposition and mimicking theorems for conditional Mckean-Vlasov equations. arXiv preprint arXiv:2004.00099, 2020. [Google Scholar]
  44. J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. I–Le cas stationnaire. Comptes Rendus Math. 343 (2006) 619–625. [CrossRef] [MathSciNet] [Google Scholar]
  45. J.-M. Lasry and P.-L. Lions, Mean field games. Jap. J. Math. 2 (2007) 229–260. [CrossRef] [Google Scholar]
  46. M. Laurière and L. Tangpi, Convergence of large population games to mean field games with interaction through controls. arXiv preprint arXiv:2004.08351, 2020. [Google Scholar]
  47. M. Motte and H. Pham, Mean–field Markov decision processes with common noise and open-loop controls. Ann. Appl. Probab. 32 (2022) 1421–1458. [CrossRef] [MathSciNet] [Google Scholar]
  48. A. Neufeld and M. Nutz, Measurability of semimartingale characteristics with respect to the probability law. Stoch. Process. Applic. 124 (2014) 3819–3845. [CrossRef] [Google Scholar]
  49. D. Possamaï and L. Tangpi, Non-asymptotic convergence rates for mean-field games: weak formulation and mckean–vlasov bsdes. arXiv preprint arXiv:2105.00484, 2021. [Google Scholar]
  50. E. Roxin, The existence of optimal controls. Michigan Math. J. 9 (1962) 109–119. [Google Scholar]
  51. D. Stroock and S. Varadhan, Multidimensional Diffusion Processes. Vol. 233 of Grundlehren der mathematischen Wissenschaften. Springer—Verlag, Berlin, Heidelberg (1997). [Google Scholar]
  52. R.F. Tchuendom, Uniqueness for linear-quadratic mean field games with common noise. Dyn. Games Applic. 8 (2018) 199–210. [CrossRef] [Google Scholar]
  53. A.J. Veretennikov, On strong solutions and explicit formulas for solutions of stochastic integral equations. Math. USSR-Sbornik 39 (1981) 387–403. [CrossRef] [Google Scholar]
  54. C. Villani, Optimal Transport: Old and New. Vol. 338 of Grundlehren der Mathematischen Wissenschafte. Springer (2008). [Google Scholar]
  55. J. Yong and J. Zhang, Non-equivalence of stochastic optimal control problems with open and closed loop controls. Syst. Control Lett. 153 (2021) 104948. [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.