Control and nash games with mean field effect

Chinese Annals of Mathematics. Series B

Volumn 34, Issue 2, 2013, Pages 161-192

  Bensoussan, Alain ^a,c,d   Frehse, Jens ^b  

^a UNIVERSITY OF TEXAS AT DALLAS   (United States)

^b HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

^c Ajou University   (South Korea)

^d UNIVERSITY OF BONN   (Germany)

Author keywords

Calculus of variations; Dynamic programming; Equilibrium; Mean field; Nash games

Indexed keywords

EID: 84875520943     PISSN: 02529599     EISSN: 18606261     Source Type: Journal    
DOI: 10.1007/s11401-013-0767-y     Document Type: Article

References (15)

1. Bensoussan, A., Bulicěk, M. and Frehse, J., Existence and Compactness for weak solutions to Bellman systems with critical growth, Discrete Contin. Dyn. Syst., Ser. B, 17(6), 2012, 1-21.
2. Bensoussan, A. and Frehse, J., Regularity results for nonlinear elliptic systems and applications, Appl. Math. Sci., 151, Springer-Verlag, Berlin, 2002.
3. Bensoussan, A. and Frehse, J., Ergodic Bellman systems for stochastic games, Markus Feestricht Volume Differential Equations, Dynamical Systems and Control Sciences, Lecture Notes in Pure and Appl. Math., K. D. Elworty, W., Norrie Everitt, E. Bruce Lee, M. Dekker (eds.), Vol. 152, 1993, 411-421.
4. Bensoussan, A. and Frehse, J., Ergodic Bellman systems for stochastic games in arbitrary dimension, Proc. Royal Soc., London, Math. Phy. Sci. A, 449, 1995, 65-67.
5. Bensoussan, A. and Frehse, J., Smooth solutions of systems of quasilinear parabolic equations, ESAIM: Control, Optimization and Calculus of Variations, 8, 2002, 169-193.
6. Bensoussan, A., Frehse, J. and Vogelgesang, J., Systems of Bellman equations to stochastic differential games with noncompact coupling, Discrete Contin. Dyn. Syst., Ser. A, 274, 2010, 1375-1390.
7. Bensoussan, A., Frehse, J. and Vogelgesang, J., Nash and stackelberg differential games, Chin. Ann. Math., 33B(3), 2012, 317-332.
8. Bulicěk, M. and Frehse, J., On nonlinear elliptic Bellman systems for a class of stochastic differential games in arbitrary dimension, Math. Models Methods Appl. Sci., 21(1), 2011, 215-240.
9. Guéant, O., Lasry, J. M. and Lions, P. L., Mean field games and applications, Paris-Princeton Lectures on Mathematical Sciences 2010, A. R. Carmona, et al. (eds.), 2011, 205-266.
10. Huang, M., Caines, P. E. and Malhamé, R. P., Large-population cost-coupled LQG problems with nonuniform agents: individual-mass behavior and decentralized ε-Nash equilibria, IEEE Trans. Automat. Control, 52(9), 2007, 1560-1571.
11. Huang, M., Caines, P. E. and Malhamé, R. P., An invariance principle in large population stochastic dynamic games, J. Syst. Sci. Comp., 20(2), 2007, 162-172.
12. Ladyzhenskaya, O. A. and Uraltseva, N. N., Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968.
13. Lasry, J. M. and Lions, P. L., Jeux champ moyen I-Le cas stationnaire, Comptes Rendus de l'Académie des Sciences, Series I, 343, 2006, 619-625.
14. Lasry, J. M. and Lions, P. L., Jeux à champ moyen II-Horizn fini et contrôle optimal, Comptes Rendus de l'Académie des Sciences, Series I, 343, 2006, 679-684.
15. Lasry, J. M. and Lions, P. L., Mean field games, Japanese J. Math., 2(1), 2007, 229-260.