Open Access
Volume 57, Number 2, March-April 2023
Page(s) 953 - 990
Published online 07 April 2023
  1. Y. Achdou and I. Capuzzo-Dolcetta, Mean field games: numerical methods. SIAM J. Numer. Anal. 48 (2010) 1136–1162. [Google Scholar]
  2. Y. Achdou and M. Lauriére, Mean field games and applications: numerical aspects, in Mean field games: Cetraro, Italy 2019, Edited by P. Cardaliaguet and A. Porretta. Springer International Publishing (2020) 249–307. [CrossRef] [Google Scholar]
  3. R. Aïd, R. Dumitrescu and P. Tankov, The entry and exit game in the electricity markets: A mean-field game approach. J. Dyn. Games 8 (2021) 331–358. [CrossRef] [MathSciNet] [Google Scholar]
  4. C. Aliprantis and K. Border, Infinite Dimensional Analysis: A Hitchhiker’s Guide. Springer (2007). [Google Scholar]
  5. A. Angiuli, C. Graves, H. Li, J.-F. Chassagneux, F. Delarue and R. Carmona, CEMRACS 2017: numerical probabilistic approach to MFG. ESAIM ProcS 65 (2017) 84–113. [Google Scholar]
  6. Y. Ashrafyan, T. Bakaryan, D. Gomes and J. Gutierrez, A duality approach to a price formation MFG model. Preprint arXiv:2109.01791 (2021). [Google Scholar]
  7. A. Bensoussan and J.-L. Lions, Applications of variational inequalities in stochastic control, North Holland Publishing Company (1982). [Google Scholar]
  8. C. Bertucci, Optimal stopping in mean field games, an obstacle approach. J. Math. Pures Appl. 120 (2017) 165–194. [Google Scholar]
  9. C. Bertucci, A remark on Uzawa’s algorithm and an application to mean field games systems. ESAIM: M2AN 54 (2020) 1053–1071. [CrossRef] [EDP Sciences] [Google Scholar]
  10. A. Biryuk and D. Gomes, An introduction to the Aubry-Mather theory. São Paulo J. Math. Sci. 4 (2010) 17–63. [CrossRef] [MathSciNet] [Google Scholar]
  11. V. Bogachev, Measure Theory, Springer Science & Business Media (2007). [CrossRef] [Google Scholar]
  12. G. Bouveret, R. Dumitrescu and P. Tankov, Mean-field games of optimal stopping: a relaxed solution approach. SIAM J. Control Optim. 58 (2020) 1795–1821. [CrossRef] [MathSciNet] [Google Scholar]
  13. G. Bouveret, R. Dumitrescu and P. Tankov, Technological change in water use: a mean-field game approach to optimal investment timing. Oper. Res. Perspect. 9 (2022) 100225. [Google Scholar]
  14. G. Brown, Iterative solution of games by fictitious play. Act. Anal. Prod. Alloc. 13 (1951) 374–376. [Google Scholar]
  15. M. Burzoni and L. Campi, Mean field games with absorption and common noise with a model of bank run. Preprint arXiv:2107.00603 (2021). [Google Scholar]
  16. L. Campi and M. Fischer, N-player games and mean-field games with absorption. Ann. Appl. Prob. 28 (2018) 2188–2242. [CrossRef] [Google Scholar]
  17. L. Campi, M. Ghio and G. Livieri, N-player games and mean-field games with smooth dependence on past absorptions. Ann. Inst. Henri Poincare Probab. Stat. 57 (2021) 1901–1939. [MathSciNet] [Google Scholar]
  18. P. Cardaliaguet and S. Hadikhanloo, Learning in mean field games: the fictitious play. ESAIM: COCV 23 (2017) 569–591. [EDP Sciences] [Google Scholar]
  19. J.-F. Chassagneux, D. Crisan and F. Delarue, Numerical method for FBSDEs of McKean–Vlasov type. Ann. Appl. Prob. 29 (2019) 1640–1684. [Google Scholar]
  20. X. Chen, L. Cheng, J. Chadam and D. Saunders, Existence and uniqueness of solutions to the inverse boundary crossing problem for diffusions. Ann. Appl. Prob. 21 (2011) 1663–1693. [CrossRef] [Google Scholar]
  21. M.J. Cho and R.H. Stockbridge, Linear programming formulation for optimal stopping problems. SIAM J. Control Optimiz. 40 (2002) 1965–1982. [CrossRef] [Google Scholar]
  22. J. Claisse, Z. Ren and X. Tan, Mean field games with branching. Preprint arXiv:1912.11893 (2019). [Google Scholar]
  23. J. Dianetti, G. Ferrari, M. Fischer and M. Nendel, A unifying framework for submodular mean field games. Preprint arXiv:2201.07850 (2022). [Google Scholar]
  24. R. Dumitrescu, M. Leutscher and P. Tankov, Control and optimal stopping mean field games: a linear programming approach. Electron. J. Probab. 26 (2021) 1–49. [CrossRef] [MathSciNet] [Google Scholar]
  25. R. Elie, J. Pérolat, M. Laurière, M. Geist and O. Pietquin, On the convergence of model free learning in mean field games. AAAI 34 (2020) 7143–7150. [CrossRef] [Google Scholar]
  26. W. Fleming and D. Vermes, Generalized solutions in the optimal control of diffusions, in Stochastic Differential Systems, Stochastic Control Theory and Applications, Springer, New York (1988) 119–127. [CrossRef] [Google Scholar]
  27. D. Gomes, A stochastic analogue of Aubry-Mather theory. Nonlinearity 15 (2002) 581–603. [Google Scholar]
  28. S. Hadikhanloo, Learning in anonymous nonatomic games with applications to first-order mean field games. Preprint arXiv:1704.00378 (2017). [Google Scholar]
  29. S. Hadikhanloo and F.J. Silva, Finite mean field games: fictitious play and convergence to a first order continuous mean field game. J. Math. Pures Appl. 132 (2019) 369–397. [CrossRef] [MathSciNet] [Google Scholar]
  30. 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 (2006) 221–252. [CrossRef] [MathSciNet] [Google Scholar]
  31. S.D. Jacka, Local times, optimal stopping and semimartingales. Ann. Prob. 21 (1993) 329–339. [CrossRef] [Google Scholar]
  32. J. Jacod and J. Mémin, Sur un type de convergence intermédiaire entre la convergence en loi et la convergence en probabilité. Sém. Probab. Strasbourg 15 (1981) 529–546. [Google Scholar]
  33. I. Karatzas and S. Shreve, Brownian Motion and Stochastic Calculus, Springer-Verlag, New York (1998). [CrossRef] [Google Scholar]
  34. I. Karatzas and S. Shreve, Methods of Mathematical Finance, Springer-Verlag, New York (1998). [Google Scholar]
  35. T. Kurtz and R.H. Stockbridge, Existence of Markov controls and characterization of optimal Markov controls. SIAM J. Control Optimiz. 36 (1998) 609–653. [CrossRef] [Google Scholar]
  36. T.G. Kurtz and R.H. Stockbridge, Linear programming formulations of singular stochastic control problems: time-homogeneous problems. Preprint arXiv:1707.09209 (2017). [Google Scholar]
  37. H. Kushner and P.G. Dupuis, Numerical Methods for Stochastic Control Problems in Continuous Time, Springer New York (2001). [CrossRef] [Google Scholar]
  38. D. Lacker, Mean field games via controlled martingale problems: existence of Markovian equilibria. Stoch. Process. Appl. 125 (2015) 2856–2894. [CrossRef] [Google Scholar]
  39. J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. I. Le cas stationnaire. C. R. Math. 343 (2006) 619–625. [CrossRef] [MathSciNet] [Google Scholar]
  40. J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. II. Horizon fini et contrôle optimal. C. R. Math. 343 (2006) 679–684. [CrossRef] [MathSciNet] [Google Scholar]
  41. J.-M. Lasry and P.-L. Lions, Mean field games. Jpn. J. Math. 2 (2007) 229–260. [Google Scholar]
  42. R.M. Lewis and R.B. Vinter, Relaxation of optimal control problems to equivalent convex programs. J. Math. Anal. Appl. 74 (1980) 475–493. [CrossRef] [MathSciNet] [Google Scholar]
  43. R. Mañé, Generic properties and problems of minimizing measures of Lagrangian systems. Nonlinearity 9 (1996) 273–310. [CrossRef] [MathSciNet] [Google Scholar]
  44. J.N. Mather, Action minimizing invariant measures for positive definite Lagrangian systems. Math. Z. 207 (1991) 169–207. [CrossRef] [MathSciNet] [Google Scholar]
  45. M. Mendiondo and R. Stockbridge, Approximation of infinite-dimensional linear programming problems which arise in stochastic control. SIAM J. Control Optimiz. 36 (1998) 1448–1472. [CrossRef] [Google Scholar]
  46. J.R. Munkres, Topology, 2nd ed., Prentice Hall (2000). [Google Scholar]
  47. S. Perrin, J. Perolat, M. Laurière, M. Geist, R. Elie and O. Pietquin, Fictitious play for mean field games: continuous time analysis and applications, Preprint arXiv:2007.03458 (2020). [Google Scholar]
  48. G. Peskir and A. Shiryaev, Optimal Stopping and Free-Boundary Problems, Springer (2006). [Google Scholar]
  49. R. Rossi and G. Savaré, Tightness, integral equicontinuity and compactness for evolution problems in Banach spaces. Ann. Sc. Norm. Sup. Pisa 2 (2003) 395–431. [Google Scholar]
  50. C. Villani, Topics in optimal transportation, in Graduate Studies in Mathematics, American Mathematical Society (2003). [CrossRef] [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.

Recommended for you