Explicit solutions of one-dimensional, first-order, stationary mean-field games with congestion

2016 IEEE 55th Conference on Decision and Control, CDC 2016

Volumn , Issue , 2016, Pages 4534-4539

  Gomes, Diogo A ^a   Nurbekyan, Levon ^a   Prazeres, Mariana ^a  

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

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85010789894     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2016.7798959     Document Type: Conference Paper

References (23)

1. D. Bauso, X. Zhang, and A. Papachristodoulou. Density flow over networks: A mean-field game theoretic approach. volume 2015-February, pages 3469-3474, 2014.
2. S. Cacace, F. Camilli, and C Marchi. A numerical method for mean field games on networks. preprint, 2015.
3. F. Camilli, E. Carlini, and C Marchi. A model problem for mean field games on networks. Discrete Contin. Dyn. Syst., 35(9):4173-4192, 2015.
4. M Cirant. Multi-population mean field games systems with Neumann boundary conditions. To appear in J. Math. Pures Appl., 2014.
5. R. Ferreira and D. Gomes. Existence of weak solutions for stationary mean-field games through variational inequalities. Preprint.
6. D. Gomes and H. Mitake. Existence for stationary meanfield games with congestion and quadratic Hamiltonians. NoDEA Nonlinear Differential Equations Appl., 22(6):1897-1910, 2015.
7. D. Gomes, L. Nurbekyan, and M. Prazeres. Explicit solutions of one-dimensional first-order stationary mean-field games with a generic nonlinearity. Preprint, 2016.
8. D. Gomes and S. Patrizi. Weakly coupled mean-field game systems. Preprint.
9. D. Gomes and S. Patrizi. Obstacle mean-field game problem. Interfaces Free Bound., 17(1):55-68, 2015.
10. D. Gomes, S. Patrizi, and V. Voskanyan. On the existence of classical solutions for stationary extended mean field games. Nonlinear Anal., 99:49-79, 2014.
11. D. Gomes, E. Pimentel, and V. Voskanyan. Regularity theory for mean-field game systems. 2016.
12. D. Gomes, G. E. Pires, and H. Sánchez-Morgado. A-priori estimates for stationary mean-field games. Netw. Heterog. Media, 7(2):303-314, 2012.
13. D. Gomes and R. Ribeiro. Mean field games with logistic population dynamics. 52nd IEEE Conference on Decision and Control (Florence, December 2013), 2013.
14. D. Gomes and H. Sánchez Morgado. A stochastic Evans-Aronsson problem. Trans. Amer. Math. Soc., 366(2):903-929, 2014.
15. D. Gomes and V. Voskanyan. Short-time existence of solutions for mean-field games with stion. To appear J. London Math. Soc.
16. J. Graber. Weak solutions for mean field games with congestion. Preprint, 2015.
17. M. Huang, P. E. Caines, and R. P. Malhamé. Largepopulation cost-coupled LQG problems with nonuniform agents: individual-mass behavior and decentralized -Nash equilibria. IEEE Trans. Automat. Control, 52(9):1560-1571, 2007.
18. 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(3):221-251, 2006.
19. J.-M. Lasry and P.-L. Lions. Jeux à champ moyen. I. Le cas stationnaire. C. R. Math. Acad. Sci. Paris, 343(9):619-625, 2006.
20. J.-M. Lasry and P.-L. Lions. Jeux à champ moyen. II. Horizon fini et controle optimal. C. R. Math. Acad. Sci. Paris, 343(10):679-684, 2006.
21. J.-M. Lasry and P.-L. Lions. Mean field games. Jpn. J. Math., 2(1):229-260, 2007.
22. E. Pimentel and V. Voskanyan. Regularity for second-order stationaty mean-field games. To appear in Indiana University Mathematics Journal.
23. V. K. Voskanyan. Some estimates for stationary extended mean field games. Dokl. Nats. Akad. Nauk Armen., 113(1):30-36, 2013.