Extended deterministic mean-field games

SIAM Journal on Control and Optimization

Volumn 54, Issue 2, 2016, Pages 1030-1055

  Gomes, Diogo A ^a   Voskanyan, Vardan K ^a  

^a KING ABDULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Saudi Arabia)

Author keywords

Deterministic control; Differential games; Hamilton Jacobi equations; Mean field games; Random variables methods

Indexed keywords

MATHEMATICAL TECHNIQUES; OPTIMIZATION;

COLLECTIVE BEHAVIOR; DIFFERENTIAL GAMES; EXISTENCE RESULTS; HAMILTON - JACOBI EQUATIONS; MASTER EQUATIONS; MEAN FIELD; MEAN FIELD GAMES;

RANDOM VARIABLES;

EID: 84964876681     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/130944503     Document Type: Article

References (25)

1. M. Bardi and I. Capuzzo-Dolcetta, Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, with appendices by M. Falcone and P. Soravia, Birkhaüser Boston Inc., Boston, 1997.
2. P. Cardaliaguet, Notes on mean-field games, https://www.ceremade.dauphine.fr/?cardalia/MFG100629.pdf, 2012.
3. P. Cardaliaguet, P. Garber, A. Porretta, and D. Tonon, Second Order Mean Field Games with Degenerate Diffusion and Local Coupling, NoDEA Nonlinear Differential Equations Appl. 22 (2015), pp. 1287-1317.
4. R. Carmona and F. Delarue, Mean field forward-backward stochastic differential equations, Electron. Commun. Probab., 18 (2013), 68.
5. R. Carmona and F. Delarue, Probabilistic analysis of mean-field games, SIAM J. Control Optim., 51 (2013), pp. 2705-2734.
6. R. Carmona, F. Delarue, and D. Lacker, Mean Field Games with Common Noise, preprint, arXiv:1407.6181, 2013.
7. W. H. Fleming and H. M. Soner, Controlled Markov Processes and Viscosity Solutions, 2nd ed., Stoch. Model. Appl. Probab. 25, Springer-Verlag, New York, 2006.
8. D. A. Gomes, S. Patrizi, and V. Voskanyan, On the existence of c lassical solutions for stationary extended mean field games, Nonlinear Anal., 99 (2014), pp. 49-79.
9. D. A. Gomes and E. Pimentel, Time dependent mean-field games with logarithmic nonlinearities, SIAM J. Math. Anal., 47 (2015), pp. 3798-3812.
10. D. Gomes and E. Pimentel, Local regularity for mean-field games in the whole space, Minimax Theory and Its Applications, to appear.
11. D. Gomes, E. Pimentel, and H. Sánchez-Morgado, Time dependent mean-field games in the superquadratic case, ESAIM Control Optim. Calc. Var., to appear.
12. D. A. Gomes, E. Pimentel, and H. Sánchez-Morg ado, Time-dependent mean-field games in the subquadratic case, Comm. Partial Differential Equations, 40 (2015), pp. 40-76.
13. D. Gomes, E. Pimentel, and V. Voskanyan, Regularity theory for mean-fie ld game systems, Springer Briefs in Mathematics, to appear.
14. D. Gomes,J. Saúde Mean field games models-A brief survey Dyn. Games Appl. 4 2014, 110-154.
15. 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), pp. 1 560-1571.
16. 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), pp. 221-251.
17. J.-M. Lasry and P.-L. Lions, Jeux á champ moyen. I. Le cas stationnaire, C. R. Math. Acad. Sci. Paris, 343 (2006), pp. 619-625.
18. J.-M. Lasry and P.-L. Lions, Jeux á champ moyen. II. Horizon fini et contr ole optimal, C. R. Math. Acad. Sci. Paris, 343 (2006), pp. 679-684.
19. J.-M. Lasry and P.-L. Lions, Mean field games, Jpn. J. Math., 2 (2007), pp. 229-260.
20. J.-M. Lasry and P.-L. Lions, Mean field games, Cahiers de la Chaire Finance et Développement Durable, 2007.
21. J.-M. Lasry, P.-L. Lions, and O. Guéant, Mean field games and applications, in Paris-Princeton Lectures on Mathematical Finance 2010, Lecture Notes in Math. 2003, Springer, Berlin, 2011, pp. 205-266.
22. P.-L. Lions, Collége de France-Course on Mean-Field Games, http://www.college-de-france. fr/site/en-pierre-louis-lions/(2007-2011).
23. A. Porretta, On the planning problem for the mean field games system, Dyn. Games Appl., 4 (2014), pp. 231-256.
24. A. Porretta, Weak solutions to Fokker-Planck equations and mean field games, Arch. Ration. Mech. Anal., 216 (2015), pp. 1-62.
25. C. Villani, Topics in Optimal Transportation, Grad. Stud. Math. 58, American Mathematical Society, Providence, RI, 2003.