Mean-field games and two-point boundary value problems

Proceedings of the IEEE Conference on Decision and Control

Volumn 2015-February, Issue February, 2014, Pages 2722-2727

  Mylvaganam, Thulasi ^a   Bauso, Dario ^a   Astolfi, Alessandro ^b  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b UNIVERSITY OF PALERMO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; DYNAMIC PROGRAMMING; PARTIAL DIFFERENTIAL EQUATIONS;

FOKKER-PLANK-KOLMOGOROV EQUATIONS; HAMILTON JACOBI BELLMAN EQUATION; LARGE POPULATION; LOW DENSITY; MEAN FIELD GAMES; TWO POINT BOUNDARY VALUE; TWO POINT BOUNDARY VALUE PROBLEMS; VALUE FUNCTIONS;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 84988267436     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2014.7039806     Document Type: Conference Paper

References (23)

1. D. Acemoʇlu, G. Como, F. Fagnani, and A. Ozdaglar. Opinion fluctuations and disagreement in social networks. Math. of Operation Research, Vol. 38, no. 1, pp. 1-27, 2013.
2. D. Acemoʇlu, A. Ozdaglar. Opinion dynamics and learning in social networks. International Review of Economics, Vol. 1, no. 1, pp. 3-49, 2011.
3. Y. Achdou, F. Camilli, and I. Capuzzo Dolcetta. Mean field games: numerical methods for the planning problem. SIAM J. of Control Opt., Vol. 50, pp. 77-109, 2012.
4. F. Bagagiolo, and D. Bauso. Mean-field games and dynamic demand management in power grids. Dynamic Games and Applications, in print.
5. M. Bardi. Explicit solutions of some Linear-Quadratic Mean Field Games. Network and Heterogeneous Media, 7, pp. 243-261, 2012.
6. D. Bauso, H. Tembine, and T. Başar. Robust Mean Field Games with Application to Production of an Exhaustible Resource. Proc. of 7th IFAC Symposium on Robust Control Design, Aalborg, Denmark, 2012.
7. D. Bauso, Q. Zhu and T. Başar. Mixed Integer Optimal Compensation: Decompositions and Mean-Field Approximations. Proc. of 2012 American Control Conference, Montreal, Montreal, Canada, 2012.
8. D. Bauso, T. Mylvaganam, and A. Astolfi. Approximate solutions for crowd-averse robust mean-field games. European Control Conference, 2013.
9. D. Bauso, T. Mylvaganam, and A. Astolfi. A two-point boundary value formulation of a mean-field crowd-averse game. The 19th World Congress of the International Federation of Automatic Control, 2013.
10. C. Castellano, S. Fortunato, and V. Loreto. Statistical physics of social dynamics. Rev. Mod. Phys., Vol. 81, pp. 591-646, 2009.
11. G. Como, F. Fagnani. Scaling limits for continuous opinion dynamics systems. The Annals of Applied Probability, Vol. 21, no. 4, pp. 1537-1567.
12. O. Gueant, J. M. Lasry, and P. L. Lions. Mean-field games and applications. Paris-Princeton Lectures, Springer, pp. 1-66, 2010.
13. M.Y. Huang, P.E. Caines, and R.P. Malhamé. Large Population Stochastic Dynamic Games: Closed Loop Kean-Vlasov Systems and the Nash Certainty Equivalence Principle. Communications in Information and Systems, Vol. 6, no. 3, pp. 221-252, 2006.
14. M.Y. Huang, P.E. Caines, and R.P Malhamé. Large population cost-coupled LQG problems with non-uniform agents: individual-mass behaviour and decentralized ε-Nash equilibria IEEE Trans. on Automatic Control, Vol. 52. no. 9, pp. 1560-1571, 2007.
15. M.Y. Huang, P.E. Caines, and R.P. Malhamé. Individual and Mass Behaviour in Large Population Stochastic Wireless Power Control Problems: Centralized and Nash Equilibrium. 42nd IEEE Conference on Decision and Control, Vol. 1., pp. 98-103, 2003.
16. U. Krause. A discrete nonlinear and non-autonomous model of consensus formation. Communications in Difference Equations, S. Elaydi, G. Ladas, J. Popenda, and J. Rakowski editors, Gordon and Breach, Amsterdam, pp. 227-236, 2000.
17. A. Lachapelle, J. Salomon, and G. Turinici. Computation of Mean Field Equilibria in Economics. Math. Models Meth. Appl. Sci., Vol. 20, pp. 1-22, 2010.
18. J.-M. Lasry, and P.-L. Lions. Mean field games. Japanese J. Math., Vol. 2, pp. 229-260, 2007.
19. K. A. Loparo, and X. Feng. Stability of stochastic systems. The Control Handbook, CRC Press, pp. 1105-1126, 1996.
20. R. Pesenti, and D. Bauso. Mean Field Linear Quadratic Games with Set Up Costs. Dynamic Games and Applications, Vol. 3, no. 1, pp. 89-104, March 2013.
21. A.-S. Sznitman. Topics in propagation of chaos. Springer Lecture Notes in Mathematics, Vol. 1464, pp. 165-251, 1991.
22. H. Tembine, Q. Zhu, and T. Başar. Risk-sensitive mean-field stochastic differential games. Proc. of 2011 IFAC World Congress, Milan, Italy, August 29 - September 2, 2011.
23. H. Tembine, J. Y. Le Boudec, R. ElAzouzi, E. Altman. Mean field asymptotic of Markov decision evolutionary games. IEEE Gamenets 2009.