Socio-economic applications of finite state mean field games

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 372, Issue 2028, 2014, Pages

  Gomes, Diogo ^a   Velho, Roberto M ^a   Wolfram, Marie Therese ^b  

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

^b JOHANN RADON INSTITUTE FOR COMPUTATIONAL AND APPLIED MATHEMATICS   (Austria)

Author keywords

Finite state space; Mean field games; Numerical methods; Socio economic applications

Indexed keywords

PARTIAL DIFFERENTIAL EQUATIONS;

CONSUMER CHOICE; FINITE STATE SPACES; HYPERBOLIC SYSTEM; MEAN FIELD GAMES; NUMERICAL EXPERIMENTS; SCIENTIFIC COMMUNITY; SHOCK FORMATION; SOCIO-ECONOMICS;

NUMERICAL METHODS;

EID: 84907863230     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2013.0405     Document Type: Article

References (25)

1. Lions P-L. 2007-2011 Collège de France course on mean-field games. See http://www. college-de-france.fr/site/pierre-louis-lions/#course.
2. Gomes D, Mohr J, Souza RR. 2010 Discrete time, finite state space mean field games. J. Math. Pures Appl. 93, 308-328. (doi:10.1016/j.matpur.2009.10.010)
3. Guéant O. 2011 Existence and uniqueness result for mean field games with congestion effect on graphs. (http://arxiv.org/abs/1110.3442)
4. Guéant O. 2011 From infinity to one: the reduction of some mean field games to a global control problem. (http://arxiv.org/abs/1110.3441)
5. Gomes D, Mohr J, Souza RR. 2013 Continuous time finite state mean-field games. Appl. Math. Optim. 68, 99-143. (doi:10.1007/s00245-013-9202-8)
6. Ferreira R, Gomes DA. 2014 On the convergence of finite state mean-field games through F-convergence. J. Math. Anal. Appl. 418, 211-230. (doi:10.1016/j.jmaa.2014.02.044)
7. Lasry J-M, Lions P-L. 2006 Jeux à champ moyen. I. Le cas stationnaire. C. R. Math. Acad. Sci. Paris 343, 619-625. (doi:10.1016/j.crma.2006.09.019)
8. Lasry J-M, Lions P-L. 2006 Jeux à champ moyen. II. Horizon fini et contrôle optimal. C. R. Math. Acad. Sci. Paris 343, 679-684. (doi:10.1016/j.crma.2006.09.018)
9. Lasry J-M, Lions P-L. 2007 Mean field games. Jpn. J. Math. 2, 229-260. (doi:10.1007/s11537-007-0657-8)
10. Huang M, Malhamé RP, Caines PE. 2006 Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle. Commun. Inform. Syst. 6, 221-251. (doi:10.4310/CIS.2006.v6.n3.a5)
11. Huang M, Caines PE, Malhamé RP. 2007 Large-population cost-coupled LQG problems with nonuniform agents: individual-mass behavior and decentralized ∈-Nash equilibria. IEEE Trans. Automat. Control 52, 1560-1571. (doi:10.1109/TAC.2007.904450)
12. Lasry J-M, Lions P-L, Guéant O. 2011 Mean field games and applications. In Paris-Princeton lectures on mathematical finance 2010. Lecture Notes in Mathematics, vol. 2003, pp. 205-266. Berlin, Germany: Springer. (doi:10.1007/978-3-642-14660-2-3)
13. Cardaliaguet P. 2011 Notes on mean field games (from P.-L. Lions' lectures at Collège de France). See http://www.ceremade.dauphine.fr/~cardalia/MFG100629.pdf.
14. Achdou Y. 2013 Finite difference methods for mean field games. In Hamilton-Jacobi equations: approximations, numerical analysis and applications. Lecture Notes in Mathematics, vol. 2074, pp. 1-47. Berlin, Germany: Springer. (doi:10.1007/978-3-642-36433-4-1)
15. Gomes D, Saude J. 2013 Mean-field games: a brief survey. Dyn. Games Appl. 4, 110-154. (doi:10.1007/s13235-013-0099-2)
16. Bensoussan A, Frehse J, Yam P. 2013 Mean field games and mean field type control theory. Springer Briefs in Mathematics. New York, NY: Springer.
17. Besancenot D, Dogguy H. In press. Paradigm shift: a mean-field game approach. Bull. Econ. Res. (doi:10.1111/boer.12024)
18. Kuhn TS. 1970 The structure of scientific revolutions. Chicago, IL: University of Chicago Press.
19. Brock WA, Durlauf SN. 1999 A formal model of theory choice in science. Econ. Theory 14, 113-130. (doi:10.1007/s001990050284)
20. Bramoullé Y, Saint-Paul G. 2010 Research cycles. J. Econ. Theory 145, 1890-1920. (doi:10.1016/j.jet.2010.02.004)
21. Guéant O. 2006 Mean field games and applications to economics. PhD thesis, Université Paris Dauphine, Paris.
22. Abgrall R. 2003 Numerical discretization of boundary conditions for first order Hamilton-Jacobi equations. SIAM J. Numer. Anal. 41, 2233-2261. (doi:10.1137/S0036142998345980)
23. Waagan K. 2008 Convergence rate of monotone numerical schemes for Hamilton-Jacobi equations with weak boundary conditions. SIAM J. Numer. Anal. 46, 2371-2392. (doi:10.1137/050632932)
24. Kurganov A, Tadmor E. 2000 New high-resolution semi-discrete central schemes for Hamilton-Jacobi equations. J. Comput. Phys. 160, 720-742. (doi:10.1006/jcph.2000.6485)
25. Kurganov A, Tadmor E. 2000 New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations. J. Comput. Phys. 160, 241-282. (doi:10.1006/jcph.2000.6459)