Learning in mean field games: The fictitious play

ESAIM - Control, Optimisation and Calculus of Variations

Volumn 23, Issue 2, 2017, Pages 569-591

  Cardaliaguet, Pierre ^a   Hadikhanloo, Saeed ^a  

^a UNIVERSITÉ PARIS DAUPHINE   (France)

Author keywords

Learning; Mean field games

Indexed keywords

OPTIMIZATION;

DIFFERENTIAL GAMES; EQUILIBRIUM CONFIGURATION; FICTITIOUS PLAY; INTERACTING AGENTS; LEARNING; LEARNING PROCEDURES; MEAN FIELD GAMES; NOCV1;

CONTROL;

EID: 85011536691     PISSN: 12928119     EISSN: 12623377     Source Type: Journal    
DOI: 10.1051/cocv/2016004     Document Type: Article

References (28)

1. Y. Achdou, F.J. Buera, J.M. Lasry, P.L. Lions, and B. Moll, Partial differential equation models in macroeconomics. Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci. 372 (2014) 20130397.
2. S.R. Aiyagari, Uninsured Idiosyncratic Risk and Aggregate Saving. The Quarterly Journal of Economics 109 (1994) 659-84.
3. L. Ambrosio, Transport equation and Cauchy problem for BV vector fields. Inv. Math. 158 (2004) 227-260.
4. L. Ambrosio, N. Gigli, and G. Savarè, Gradient flows in metric spaces and in the space of probability measures. Lectures in Mathematics ETH Zürich. Birkhäuser-Verlag, Basel (2008).
5. G.W. Brown, Iterative solution of games by Fictitious Play. Activity Anal. Prod. Alloc. 13 (1951) 374-376.
6. P. Cannarsa, and C. Sinestrari, Semiconcave functions, Hamilton-Jacobi equations and optimal control. Birkhäuser, Boston (2004).
7. P. Cardaliaguet, Weak solutions for first order mean field games with local coupling. Preprint hal-00827957.
8. P. Cardaliaguet, Long time average of first order mean field games and weak KAM theory. Dyn. Games Appl. 3 (2013) 473-488.
9. P. Cardaliaguet, G. Carlier, and B. Nazaret, Geodesics for a class of distances in the space of probability measures. Calc. Var. Partial Differ. Eq. 48 (2013) 395-420.
10. P. Cardaliaguet, F. Delarue, J.-M. Lasry, and P.-L. Lions, The master equation and the convergence problem in mean field games. Preprint arXiv:1509.0205 (2015).
11. P. Cardaliaguet, J. Graber, A. Porretta, and D. Tonon, Second order mean field games with degenerate diffusion and local coupling. Nonlin. Differ. Equ. Appl. 22 (2015) 1287-1317.
12. R. Carmona, and F. Delarue, Probabilist analysis of Mean-Field Games. SIAM J. Control Optim. 51 (2013) 2705-2734.
13. R.-J. DiPerna, and P.-L. Lions, Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math. 98 (1989) 511-547.
14. O. Guéant, Mean field games equations with quadratic hamiltonian: a specific approach. Math. Models Methods Appl. Sci. 22 (2012) 1250022.
15. O. Guéant, P.-L. Lions, and J.-M. Lasry, Mean Field Games and Applications. Paris-Princeton Lectures on Mathematical Finance 2010, edited by P. Tankov, P.-L. Lions, J.-P. Laurent, J.-M. Lasry, M. Jeanblanc, D. Hobson, O. Guéant, S. Crépey, A. Cousin. Springer, Berlin (2011) 205-266.
16. D. Fudenberg, and D.K. Levine, The theory of learning in games. MIT Press, Cambridge, MA (1998).
17. M. Huang, P.E. Caines, and R.P. Malhamé, Individual and mass behaviour in large population stochastic wireless power control problems: centralized and Nash equilibrium solutions. Proc. of 42nd IEEE Conf. Decision Contr., Maui, Hawaii (2003) 98-103.
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. Inform. Syst. 6 (2006) 221-252.
19. O.A. Ladyženskaja, V.A. Solonnikov, and N.N. Ural'ceva, Linear and quasilinear equations of parabolic type. In vol. 23 of Translations of Mathematical Monographs. American Mathematical Society, Providence, R.I. (1967).
20. J.-M. Lasry, and P.-L. Lions, Jeux à champ moyen. I. Le cas stationnaire. C. R. Math. Acad. Sci. Paris 343 (2006) 619-625.
21. J.-M. Lasry, and P.-L. Lions, Jeux à champ moyen. II. Horizon fini et contrôle optimal. C. R. Math. Acad. Sci. Paris 343 (2006) 679-684.
22. J.-M. Lasry, and P.-L. Lions, Mean field games. Jpn J. Math. 2 (2007) 229-260.
23. P.L. Lions, Cours au Collège de France. Available at www.college-de-france.fr.
24. K. Miyasawa, On the convergence of the learning process in a 2 '2 non-zero-sum two-person game. Princeton University, NJ (1961).
25. D. Monderer, and L.S. Shapley, Potential games. Games Econ. Behav. 14 (1996) 124-143.
26. D. Monderer, and L.S. Shapley, Fictitious play property for games with identical interests. J. Econ. Theory 68 (1996) 258-265.
27. J. Robinson, An iterative method of solving a game. Ann. Math. (1951) 296-301.
28. L.S. Shapley, Some topics in two-person games. Ann. Math. Stud. 5 (1964) 1-28.