Free Access
Volume 26, 2020
Article Number 11
Number of page(s) 38
Published online 14 February 2020
  1. R.F. Anderson and S. Orey, Small random perturbation of dynamical systems with reflecting boundary. Nagoya Math. J. 60 (1976) 189–216. [CrossRef] [Google Scholar]
  2. F. Avram and M.S. Taqqu, Probability bounds for M-Skorohod oscillations. Stoch. Process. Appl. 33 (1989) 1. [CrossRef] [Google Scholar]
  3. A. Bensoussan, J. Frehse and P. Yam, Mean field games and mean field type control theory, Vol. 101, Springer (2013). [CrossRef] [Google Scholar]
  4. P.-E. Caines, M. Huang and P. Malhamé, 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]
  5. P.-E. Caines, M. Huang and P. Malhamé, Large-population cost-coupled LQG problems with nonuniform agents: individual-mass behavior and decentralized ϵ-Nash equilibria. IEEE Trans. Automat. Control 52 (2007) 1560–1571. [CrossRef] [MathSciNet] [Google Scholar]
  6. P. Cannarsa and R. Capuani, Existence and uniqueness for Mean Field Games with state constraints, PDE Models for Multi-Agent Phenomena (2018) 49–71. [CrossRef] [Google Scholar]
  7. P. Cannarsa, R. Capuani and P. Cardaliaguet, C1,1-smoothness of constrained solutions in the calculus of variations with application to mean field games. arXiv:1806.08966 (2018). [Google Scholar]
  8. P. Cannarsa, R. Capuani and P. Cardaliaguet, Mean Field Games with state constraints: from mild to pointwise solutions of the PDE system. arXiv:1812.11374 (2018). [Google Scholar]
  9. P. Cardaliaguet and C.-A. Lehalle, Mean field game of controls and an application to trade crowding. Math. Financ. Econ. 12 (2018) 335–363. [CrossRef] [Google Scholar]
  10. P. Cardaliaguet, F. Delarue, J.-M. Lasry and P.-L. Lions, The master equation and the convergence problem in mean field games. arXiv:1509.02505v1 (2015). [Google Scholar]
  11. R. Carmona and F. Delarue, Probabilistic analysis of mean-field games. SIAM J. Cont. Optim. 51 (2013) 2705–2734. [CrossRef] [MathSciNet] [Google Scholar]
  12. R. Carmona and F. Delarue, Probabilistic theory of mean-field games with applications I–II, Vol. 83–84, Springer (2018). [Google Scholar]
  13. P. Chan and R. Sircar, Bertrand and Cournot mean field games. Appl. Math. Optim. 71 (2015) 533–569. [Google Scholar]
  14. P. Chan and R. Sircar, Fracking, renewables & mean field games. SIAM Rev. 59 (2017) 588–615. [CrossRef] [Google Scholar]
  15. M. Freidlin, Functional integration and partial differential equations. Annals of Mathematics Studies, Princeton University Press (1985). [Google Scholar]
  16. D. Fudenberg and J. Tirole, Game Theory, MIT Press (1991). [Google Scholar]
  17. D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order, Classics in Mathematics, Springer-Verlag, Berlin (2001). [Google Scholar]
  18. D. Gomes and V. Voskanyan, Extended deterministic mean-field games. SIAM J. Cont. Optim. 54 (2016) 1030–1055. [CrossRef] [Google Scholar]
  19. D. Gomes, S. Patrizi and V. Voskanyan, On the existence of classical solutions for stationary extended mean field games. Nonlin. Anal. Theory Methods Appl. 99 (2014) 49–79. [CrossRef] [Google Scholar]
  20. P.J. Graber and C. Mouzouni, Variational mean field games for market competition. arXiv:1707.07853 (2017). [Google Scholar]
  21. P.J. Graber and A. Bensoussan, Existence and uniqueness of solutions for Bertrand and Cournot mean field games. Appl. Math. Optim. 77 (2018) 47–71. [Google Scholar]
  22. O. Guéant, J.-M. Lasry and P.-L. Lions, Mean field games and applications, Paris-Princeton lectures on mathematicalfinance 2010 (2011) 205–266. [Google Scholar]
  23. B. Hambly and S. Ledger, A stochastic McKean-Vlasov equation for absorbing diffusions on the half-line. Ann. Appl. Probab. 27 (2017) 2698–2752. [Google Scholar]
  24. C. Harris, S. Howison and R. Sircar, Games with exhaustible resources. SIAM J. Appl. Math. 70 (2010) 2556–2581. [Google Scholar]
  25. V.N. Kolokoltsov, J. Li and W. Yang, Mean field games and nonlinear Markov processes. arXiv:1112.3744 (2011). [Google Scholar]
  26. O.A. Ladyzenskaja, V.A. Solonnikov and N.N. Ural’ceva, Linear and quasilinear equations of parabolic type, Translations of Mathematical Monographs, vol. 23, American Mathematical Society, Providence, R.I. (1967). [Google Scholar]
  27. J.-M. Lasry and P.-L. Lions, Jeux á champ moyen. I–Le cas stationnaire. Comptes Rendus Mathématique 343 (2006) 619–625. [CrossRef] [MathSciNet] [Google Scholar]
  28. J.-M. Lasry and P.-L. Lions, Jeux á champ moyen. II-Horizon fini et contrôle optimal. Comptes Rendus Mathématique 343 (2006) 679–684. [CrossRef] [MathSciNet] [Google Scholar]
  29. J.-M. Lasry and P.-L. Lions, Mean field games. Jpn. J. Math. 2 (2007) 229–260. [CrossRef] [MathSciNet] [Google Scholar]
  30. S. Ledger, Skorokhod’s M1 topology for distribution-valued processes. Electr. Commun. Prob. 21 (2016). [Google Scholar]
  31. A. Ledvina and R. Sircar, Dynamic Bertrand Oligopoly. Appl. Math. Optim. 63 (2011) 11–44. [Google Scholar]
  32. P.-L. Lions, Cours au Collège de France, [Google Scholar]
  33. M. Ludkovski and X. Yang, Mean Field Game Approach to Production and Exploration of Exhaustible Commodities. arXiv:1710.05131 (2017). [Google Scholar]
  34. I. Mitoma, On the sample continuity of S1-processes. J. Math. Soc. Jpn. 35 (1983) 629–636. [CrossRef] [Google Scholar]
  35. A. Porretta, Weak solutions to Fokker–Planck equations and mean field games. Arch. Ratl. Mech. Anal. 216 (2015) 1–62. [CrossRef] [MathSciNet] [Google Scholar]
  36. T. Rachev and L. Rüschendorf, Mass Transportation Problems. Vol. I: Theory; Vol. II: Applications, Probability and Its Applications, Springer-Verlag New York (1998). [Google Scholar]
  37. L.C.G. Rogers and D. Williams, Diffusions, Markov processes, and martingales. Vol. 2, Cambridge Mathematical Library. Cambridge University Press (2000). [Google Scholar]
  38. W. Whitt, Stochastic-process limits: an introduction to stochastic-process limits and their application to queues, Springer Science & Business Media (2002). [CrossRef] [Google Scholar]

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