Open Access
Issue
ESAIM: COCV
Volume 27, 2021
Article Number 85
Number of page(s) 19
DOI https://doi.org/10.1051/cocv/2021081
Published online 27 July 2021
  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, F. Camilli and I. Capuzzo Dolcetta, Mean field games: convergence of a finite difference method. SIAM J. Numer. Anal. 51 (2013) 2585–2612. [Google Scholar]
  3. Y. Achdou and M. Lauriere, On the system of partial differential equations arising in mean field type control. Discrete Contin. Dyn. Syst. 35 (2015) 3879–3900. [Google Scholar]
  4. Y. Achdou and M. Lauriere, Mean Field Games and applications: numerical aspects, in Mean field games. Vol. 2281 of Lecture Notes in Math. Springer, Cham (2020). [Google Scholar]
  5. A. Alla, M. Falcone and D. Kalise, An efficient policy iteration algorithm for dynamic programming equations. SIAM J. Sci. Comput. 37 (2015) A181–A200. [Google Scholar]
  6. M. Bardi and E. Feleqi, Nonlinear elliptic systems and mean-field games. NoDEA Nonlinear Differ. Equ. Appl. 23 (2016) 44. [Google Scholar]
  7. M. Bardi and F. Priuli, Linear-quadratic N-person and mean-field games with ergodic cost. SIAM J. Control Optim. 52 (2014) 3022–3052. [Google Scholar]
  8. R. Bellman, Dynamic Programming. Princeton Univ. Press, Princeton (1957). [Google Scholar]
  9. S. Bianchini, M. Colombo, G. Crippa and L.V. Spinolo, Optimality of integrability estimates for advection-diffusion equations. NoDEA Nonlinear Differ. Equ. Appl. 24 (2017) 33. [Google Scholar]
  10. O. Bokanowski, S. Maroso and H. Zidani, Some convergence results for Howard’s algorithm. SIAM J. Numer. Anal. 47 (2009) 3001–3026. [Google Scholar]
  11. A. Briani and P. Cardaliaguet, Stable solutions in potential mean field game systems. NoDEA Nonlinear Differ. Equ. Appl. 25 (2018), no. 1. [Google Scholar]
  12. L.M. Briceño-Arias, D. Kalise and F.J. Silva, Proximal methods for stationary mean field games with local couplings. SIAM J. Control Optim. 56 (2018) 801–836. [Google Scholar]
  13. S. Cacace and F. Camilli, A generalized Newton method for homogenization of Hamilton-Jacobi equations. SIAM J. Sci. Comput. 38 (2016) A3589–A3617. [Google Scholar]
  14. P. Cardaliaguet and S. Hadikhanloo, Learning in mean field games: the fictitious play. ESAIM: COCV 23 (2017) 569–591. [EDP Sciences] [Google Scholar]
  15. P. Cardaliaguet, J.-M. Lasry, P.-L. Lions and A. Porretta, Long time average of mean field games. Netw. Heterog. Media 7 (2012) 279–301. [Google Scholar]
  16. E. Carlini and F. Silva, A semi-Lagrangian scheme for a degenerate second order mean field game system. Discrete Contin. Dyn. Syst. 35 (2015) 4269–4292. [Google Scholar]
  17. R. Carmona and F. Lacker, Mean field games of timing and models for bank runs. Appl. Math. Optim. 76 (2017) 217–260. [Google Scholar]
  18. M. Cirant and A. Goffi, On the existence and uniqueness of solutions to time-dependent fractional MFG. SIAM J. Math. Anal. 51 (2019) 913–954. [Google Scholar]
  19. M. Cirant and A. Goffi, Lipschitz regularity for viscous Hamilton-Jacobi equations with Lp terms. Ann. Inst. H. Poincaré Anal. Non Linéaire 37 (2020) 757–784. [Google Scholar]
  20. M. Cirantand A. Goffi, On the problem of maximal Lq-regularity for viscous Hamilton-Jacobi equations. Arch. Rat. Mech. Anal. 240 (2021) 1521–1534. [Google Scholar]
  21. T. Davis, SuiteSparse, http://faculty.cse.tamu.edu/davis/suitesparse.html. [Google Scholar]
  22. W.H. Fleming, Some Markovian optimization problems. J. Math. Mech. 12 (1963) 131–140. [Google Scholar]
  23. D.A. Gomes, L. Nurbekyan and E.A. Pimentel, Economic models and mean-field games theory. IMPA Mathematical Publications, Instituto Nacional de Matemática Pura e Aplicada (IMPA), Rio de Janeiro (2015) iv+127 pp. [Google Scholar]
  24. R. Howard, Dynamic Programming and Markov Processes. MIT Press, Cambridge (1960). [Google Scholar]
  25. M. Huang, P.E. Caines and R.P. Malhame, Large-population cost-coupled LQG problems with non uniform agents: Individual-mass behaviour and decentralized ϵ-Nash equilibria. IEEE Trans. Autom. Control 52 (2007) 1560–1571. [Google Scholar]
  26. B. Kerimkulov, D. Šiška and L. Szpruch, Exponential convergence and stability of Howards’s policy improvement algorithm for controlled diffusions. SIAM J. Control Optim. 53 (2020) 1314–1340. [Google Scholar]
  27. O.A. Ladyzenskaja, V.A. Solonnikov and N.N. Ural’ceva, Linear and quasilinear equations of parabolic type. Translated from the Russian by S. Smith. Translations of Mathematical Monographs. American Mathematical Society, Providence, R.I. (1968). [Google Scholar]
  28. J.-M. Lasry and P.-L. Lions, Mean field games. Jpn. J. Math. 2 (2007) 229–260. [Google Scholar]
  29. P.-L. Lions, Quelques remarques sur les problemes elliptiques quasilináires du second ordre. J. Analyse Math. 45 (1985) 234–54. [Google Scholar]
  30. A. Lunardi, Interpolation theory. Vol. 16 of Appunti della Scuola Normale Superiore di Pisa (Nuova Serie) (2018). [Google Scholar]
  31. G. Metafune, D. Pallara and A. Rhandi, Global properties of transition probabilities of singular diffusions. Teor. Veroyatn. Primen. 54 (2009) 116–148. [Google Scholar]
  32. A. Porretta, On the turnpike property for mean field games. Minimax Theory Appl. 3 (2018) 285–312. [Google Scholar]
  33. M.L. Puterman, On the convergence of policy iteration for controlled diffusions. J. Optim. Theory Appl. 33 (1981) 137–144. [Google Scholar]
  34. M.L. Puterman, Optimal control of diffusion processes with reflection. J. Optim. Theory Appl. 22 (1977) 103–116. [Google Scholar]
  35. M.L. Puterman and S.L. Brumelle, On the convergence of policy iteration in stationary dynamic programming. Math. Oper. Res. 4 (1979) 60–69. [Google Scholar]
  36. M.S. Santos and J. Rust, Convergence properties of policy iteration. SIAM J. Control Optim. 42 (2004) 2094–2115. [Google Scholar]
  37. H.-J. Schmeisser and H. Triebel, Topics in Fourier analysis and function spaces. A Wiley-Interscience Publication. John Wiley & Sons, Ltd., Chichester (1987). [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.