On efficiency in mean field differential games

Proceedings of the American Control Conference

Volumn , Issue , 2013, Pages 2527-2532

  Balandat, Maximilian ^a   Tomlin, Claire J ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTRAINED OPTIMIZATION; GAME THEORY;

BRAESS'S PARADOX; CONGESTION GAMES; CONTINUOUS ANALOGUES; DIFFERENTIAL GAMES; MEAN FIELD GAMES; NUMERICAL RESULTS; PDE-CONSTRAINED OPTIMIZATION; WELFARE MAXIMIZATIONS;

EFFICIENCY;

EID: 84883505403     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/acc.2013.6580214     Document Type: Conference Paper

References (15)

1. A. Bensoussan and J. Frehse, "Nonlinear elliptic systems in stochastic game theory, " Journal für die reine und angewandte Mathematik (Crelles Journal), vol. 350, pp. 23-67, 1984.
2. J.-M. Lasry and P.-L. Lions, "Mean field games, " Japanese Journal of Mathematics, vol. 2, pp. 229-260, 2007.
3. M. Huang, P. Caines, and R. Malhame, "Large-population costcoupled LQG problems with nonuniform agents: Individual-mass behavior and decentralized "-nash equilibria, " Automatic Control, IEEE Transactions on, vol. 52, no. 9, pp. 1560-1571, Sep 2007.
4. H. Yin, P. Mehta, S. Meyn, and U. Shanbhag, "On the efficiency of equilibria in mean-field oscillator games, " in American Control Conference (ACC), Jul 2011, pp. 5354-5359.
5. M. Huang, P. Caines, and R. P. Malhamé, "Social optima in mean field lqg control: Centralized and decentralized strategies, " Automatic Control, IEEE Transactions on, vol. 57, no. 7, pp. 1736-1751, 2012.
6. A. Lachapelle and M.-T. Wolfram, "On a mean field game approach modeling congestion and aversion in pedestrian crowds, " Transportation Research Part B: Methodological, vol. 45, no. 10, pp. 1572-1589, 2011.
7. T. Roughgarden and E. Tardos, "How bad is selfish routing?" J. ACM, vol. 49, no. 2, pp. 236-259, Mar 2002.
8. P.-L. Lions, "Théorie des jeux de champ moyen et applications, " Cours au Collège de France, 2008-2009.
9. O. Guéant, "A reference case for mean field games models, " Journal de Mathématiques Pures et Appliquées, vol. 92, no. 3, pp. 276-294, 2009.
10. Y. Achdou and I. Capuzzo-Dolcetta, "Mean field games: Numerical methods, " SIAM Journal on Numerical Analysis, vol. 48, no. 3, pp. 1136-1162, 2010.
11. O. Guéant, J.-M. Lasry, and P.-L. Lions, "Mean field games and applications, " in Paris-Princeton Lectures on Mathematical Finance 2010, ser. Lecture Notes in Mathematics. Springer, 2011, vol. 2003, pp. 205-266.
12. W. Fleming and H. Soner, Controlled Markov processes and viscosity solutions, 2nd ed., ser. Stochastic modelling and applied probability. Springer-Verlag, 2006.
13. A. Lachapelle, J. Salomon, and G. Turinci, "Computation of mean field equilibria in economics, " Math. Models Methods Appl. Sci., vol. 20, pp. 567-588, 2010.
14. A. Bensoussan, G. D. Prato, M. C. Delfour, and S. K. Mitter, Representation and Control of Infinite Dimensional Systems (Systems & Control: Foundations & Applications), 2nd ed. Birkhäuser, 2007.
15. T. Başar and Q. Zhu, "Prices of anarchy, information, and cooperation in differential games, " Dynamic Games and Applications, vol. 1, pp. 50-73, 2011.