Free Access
Volume 26, 2020
Article Number 33
Number of page(s) 35
Published online 21 April 2020
  1. L. Ambrosio, N. Gigli and G. Savaré, Gradient flows: in metric spaces and in the space of probability measures. Lectures in Mathematics. ETH Zurich. Birkhäuser, Basel (2005). [Google Scholar]
  2. J.-P. Aubin, Viability theory. Birkhäuser, Boston (2009). [CrossRef] [Google Scholar]
  3. J.-P. Aubin and A. Cellina, Differential inclusions. Set-valued maps and viability theory. Springer, New York (1984). [CrossRef] [Google Scholar]
  4. Y.V. Averboukh, A minimax approach to mean field games. Mat. Sb. 206 (2015) 3–32. [CrossRef] [Google Scholar]
  5. M. Bardi and M. Fischer, On non-uniqueness and uniqueness of solutions in finite-horizon mean field games. ESAIM: COCV 25 (2019) 44. [CrossRef] [EDP Sciences] [Google Scholar]
  6. A. Bensoussan, J. Frehse and P. Yam, Mean field games and mean field type control theory. Springer Briefs in Mathematics. Springer, New York (2013). [CrossRef] [Google Scholar]
  7. A. Bensoussan, J. Frehse and S. Yam, The master equation in mean field theory. J. Math. Pures Appl. 103 (2015) 1441–1474. [Google Scholar]
  8. P. Cardaliaguet, Notes on mean-field games. (2013). [Google Scholar]
  9. P. Cardaliaguet, F. Delarue, J.-M. Lasry and P.-L. Lions, The master equation and the convergence problem in mean field games. Preprint arXiv:1509.02505 (2015). [Google Scholar]
  10. R. Carmona and F. Delarue, Probabilistic analysis of mean-field games. SIAM J. Control Optim. 51 (2013) 2705–2734. [Google Scholar]
  11. R. Carmona and F. Delarue, The master equation for large population equilibriums. Stochastic Analysis and Applications, edited by D. Crisan, B. Hambly, and T. Zariphopoulou. In volume 100 of Springer Proceedings in Mathematics and Statistics Springer (2014) 77–128. [CrossRef] [Google Scholar]
  12. R. Carmona and F. Delarue, Probabilistic Theory of Mean Field Games with Applications I. Springer, New York (2018). [Google Scholar]
  13. R. Carmona and F. Delarue, Probabilistic Theory of Mean Field Games with Applications II. Springer, New York (2018). [Google Scholar]
  14. R. Carmona, F. Delarue and A. Lachapelle, Control of McKean-Vlasov dynamics versus mean field games. Math. Financ. Econ. 7 (2013) 131–166. [CrossRef] [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. [Google Scholar]
  16. M. Fischer, On the connection between symmetric n-player games and mean field games. Ann. Appl. Probab. 27 (2017) 757–810. [Google Scholar]
  17. H. Frankowska, Lower semicontinuous solutions of Hamilton-Jacobi-Bellman equations. SIAM J. Control Optim. 31 (1993) 257–272. [Google Scholar]
  18. W. Gangbo, T. Nguyen and A. Tudorascu, Hamilton-Jacobi equations in the Wasserstein space. Methods Appl. Anal. 15 (2008) 155–184. [Google Scholar]
  19. W. Gangbo and A. Świȩch, Existence of a solution to an equation arising from the theory of mean field games. J. Differ. Equ. 259 (2015) 6573–6643. [Google Scholar]
  20. W. Gangbo and A. Tudorascu, On differentiability in the Wasserstein space and well-posedness for Hamilton-Jacobi equations. J. Math. Pures Appl. 125 (2019) 119–174. [Google Scholar]
  21. D.A. Gomes, L. Nurbekyan and M. Sedjro, One-dimensional forward–forward mean-field games. Appl. Math. Optim. 74 (2016) 619–642. [Google Scholar]
  22. D.A. Gomes, E.A. Pimentel and V. Voskanyan, Regularity Theory for Mean-Field Game Systems. Springer, New York (2016). [CrossRef] [Google Scholar]
  23. M. Huang, P.E. Caines and R.P. Malhamé, Large-population cost-coupled lqg problems with nonuniform agents: individual-mass behavior and decentralized Nash equilibria. IEEE Trans. Automat. Control 52 (2007) 1560–1571. [CrossRef] [MathSciNet] [Google Scholar]
  24. 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) 221–251. [Google Scholar]
  25. V. Kolokoltsov, J.J. Li and W. Yang, Mean field games and nonlinear Markov processes. Preprint arXiv:1112.3744v2 (2011). [Google Scholar]
  26. V.N. Kolokoltsov and M. Troeva, On the mean field games with common noise and the McKean-Vlasov SPDEs. Preprint arXiv:1506.04594 (2015). [Google Scholar]
  27. D. Lacker, Mean field games via controlled martingale problems: existence of Markovian equilibria. Stochastic Process. Appl. 125 (2015) 2856–2894. [CrossRef] [Google Scholar]
  28. D. Lacker, A general characterization of the mean field limit for stochastic differential games. Probab. Theory Related Fields 165 (2016) 581–648. [CrossRef] [Google Scholar]
  29. J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. I. Le cas stationnaire. C. R. Math. Acad. Sci. Paris 343 (2006) 619–625. [CrossRef] [MathSciNet] [Google Scholar]
  30. J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. II. Horizon fini et contrôle optimal. C. R. Math. Acad. Sci. Paris 343 (2006) 679–684. [CrossRef] [MathSciNet] [Google Scholar]
  31. J.-M. Lasry and P.-L. Lions, Mean field games. Jpn. J. Math. 2 (2007) 229–260. [CrossRef] [MathSciNet] [Google Scholar]
  32. P.-L. Lions, College de France course on mean-field games. College de France (2007–2011). [Google Scholar]
  33. A. Marigonda and M. Quincampoix, Mayer control problem with probabilistic uncertainty on initial positions. J. Differ. Equ. 264 (2018) 3212–3252. [Google Scholar]
  34. S. Mayorga, Short time solution to the master equation of a first order mean field game system. Preprint arXiv:1811.08964 (2018). [Google Scholar]
  35. A.I. Subbotin, Generalized solutions of first-order PDEs. The dynamical perspective. Birkhäuser, Boston (1995). [CrossRef] [Google Scholar]
  36. A. Sznitman, Topics in propagation of chaos. Vol. 1464 of Lecture Notes in Mathematics. Springer, Berlin/Heidelberg (1991), pp. 165–251. [CrossRef] [Google Scholar]
  37. R. Viner and P. Wolenski, Hamilton-Jacobi theory for optimal control problems with data measurable in time. SIAM J. Control Optim. 28 (1990) 1404–1419. [Google Scholar]
  38. J. Warga, Optimal control of differential and functional equations. Academic Press, New York (1972). [Google Scholar]
  39. P.R. Wolenski, Hamilton-Jacobi theory for the hereditary control problems. Nonlinear Anal. 22 (1994) 875–894. [CrossRef] [Google Scholar]

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