Mean field games and applications

Lecture Notes in Mathematics

Volumn 2003, Issue , 2011, Pages 205-266

  Guéant, Olivier ^c   Lasry, Jean Michel ^a   Lions, Pierre Louis ^b  

^a UNIVERSITÉ PARIS DAUPHINE   (France)

^b l'alimentation et l'Environnement   (France)

^c NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77958476920     PISSN: 00758434     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-642-14660-2_3     Document Type: Article

References (50)

1. Abramowitz, M., Stegun, I.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York (1964)
2. Acemoglu, D., Aghion, P., Zilibotti, F.: Distance to frontier, selection, and economic growth. J. Eur. Econ. Assoc. 4 (1) (2006)
3. Achdou, Y., Capuzzo-Dolcetta, I.: Mean field games: Numerical methods (To appear)
4. Aghion, P., Bloom, N., Blundell, R., Griffith, R., Howitt, P.: Competition and innovation: An inverted-u relationship. Q. J. Econ. 120 (2) (2005)
5. Aghion, P., Harris, C., Howitt, P., Vickers, J.: Competition, imitation and growth with step-bystep innovation. Rev. Econ. Stud. 68(3), 467-492 (2001)
6. Aghion, P., Howitt, P. (To appear)
7. Atkinson, A.: Top incomes in the united kingdom over the 20th century. J. R. Stat. Soc. 168, 325-343 (2005)
8. Atkinson, A., Piketty, T.: Top Incomes over the Twentieth Century: A Contrast between European and English-Speaking Countries. Oxford University Press, Oxford (2007)
9. Aumann, R.: Markets with a continuum of traders. Econometrica 32 (1/2), 1-17 (1964)
10. Bardi, M., Capuzzo-Dolcetta, I.: Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman equations. Birkhäuser, Boston (1997)
11. Bensoussan, A., Frehse, J.: Nonlinear elliptic systems in stochastic game theory. J. Reine Angew. Math. 350, 23-67 (1984)
12. Bensoussan, A., Frehse, J.: Ergodic bellman systems for stochastic games in arbitrary dimension. Proc. Roy. Soc. A. 449, 65-77 (1995)
13. Carmona, G.: Nash equilibria of games with a continuum of players. FEUNL Working paper series no. 466 (2004)
14. Chakrabarti, B. K., Chatterjee, A., Yarlagadda, S.: Econophysics of Wealth Distributions. Springer (2005)
15. Cordier, S., Pareschi, L., Toscani, G.: On a kinetic model for a simple market economy. J. Stat. Phys. 120 (1/2), 253-277 (2005)
16. Cross, R., Grinfeld, M., Lamba, H.: A mean-field model of investor behaviour. Journal of Physics: Conference Series 55 (2006)
17. David, H. A., Nagaraja, H. N.: Order Statistics (Third edition). Wiley, New Jersey (2003)
18. Ekeland, I.: Le pétrole sera-t-il bradé? Pour la Science (2007)
19. Farkas, I., Helbing, D., Vicsek, T.: Mexican wave in an excitable medium. Nature 419, 131-132 (2002)
20. Giraud, P. N., Guéant, O., Lasry, J. M., Lions, P. L.: A mean field game model of oil production in presence of alternative energy producers (To appear)
21. Gomes, D., Mohr, J., Sousa, R.: Discrete time, finite state space mean field games. Journal de Mathématiques Pures et Appliqués 93, 308-328 (2010)
22. Guéant, O.: Mean field games and applications to economics. Ph. D. thesis, Université Paris-Dauphine (2009)
23. Guéant, O.: A reference case for mean field games. Journal de Mathématiques Pures et Appliquées 92, 276-294 (2009)
24. Guéant, O.: A reference case for mean field games. Cahier de la Chaire Finance et Développement Durable 10 (2009)
25. Guéant, O., Lasry, J. M., Lions, P. L.: Mean field games and oil production. In: Lasry, J. M., Lautier, D., Fessler, D. (eds.) The Economics of Sustainable Development. Economica (2010)
26. Guesnerie, R.: An exploration of the eductive justifications of the rational-expectations hypothesis. Am. Econ. Rev. 82(5), 1254-1278 (1992)
27. Horst, U.: Ergodic fluctuations in a stock market model with interacting agents: the mean field case. Discussion paper No. 106, Sonderforschungbereich 373, Humboldt Universität, Berlin (1999)
28. Hotelling, H.: The economics of exhaustible resources. J. Polit. Econ. 39(2), 137-175 (1931)
29. Kalai, E.: Private information in large games. Discussion paper 1312. Center for Mathematical Studies in Economics and Management Science. Northwestern University (2000)
30. Kalai, E.: Ex-post stability in large games. Discussion paper 1351. Center for Mathematical Studies in Economics and Management Science. Northwestern University (2001)
31. Kalai, E.: Large robust games. Econometrica 72 (6) (2004)
32. Khan, A., Sun, Y.: Non-cooperative games with many players (2002)
33. Lachapelle, A., Salomon, J., Turinici, G.: Computation of mean field equilibria in economics. Mathematical Models and Methods in Applied Sciences no. 1, 1-22 (2010)
34. Lasry, J. M., Lions, P. L.: Jeux à champ moyen i. le cas stationnaire. C. R. Acad. Sci. Paris 343(9), 619-625 (2006)
35. Lasry, J. M., Lions, P. L.: Jeux à champ moyen ii. horizon fini et contrôle optimal. C. R. Acad. Sci. Paris 343(10), 679-684 (2006)
36. Lasry, J. M., Lions, P. L.: Mean field games. Jpn. J. Math. 2(1), 229-260 (2007)
37. Lasry, J. M., Lions, P. L.: Mean field games. Cahiers de la Chaire Finance et Développement Durable (2) (2007)
38. Lions, P. L.: Théorie des jeux à champs moyen et applications. Cours au Collège de France, http://www.College-de-france. fr/default/EN/all/equ-der/cours-et-seminaire s.htm (2007-2008)
39. Lions, P. L.: Mathematical Topics in Fluid Mechanics. Oxford Science Publications, Clarendon Press, Oxford (Vol. 1 (1996); Vol. 2 (1998))
40. Lucas, R., Sargent, T.: Rational expectations and econometric practice. University of Minnesota Press, Minnesota (1981)
41. Markowitz, H.: Portfolio selection. J. Finance 7(1), 77-91 (1952)
42. Muth, J. F.: Rational expectations and the theory of price movements. Econometrica 29(3), 315-335 (1961)
43. Nash, J.: The bargaining problem. Econometrica 18, 155-162 (1950)
44. Nash, J.: Equilibrium points in n-person games. Proc. Natl. Acad. Sci. USA 36, 48-49 (1950)
45. Nash, J.: Non-cooperative games. Ann. Math. 54, 286-295 (1951)
46. Nash, J.: Two-person cooperative games. Econometrica 21, 128-140 (1953)
47. Neumann, J. V., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press, Princeton (1944)
48. Piketty, T.: Income inequality in france, 1901-1998. J. Polit. Econ. 111(5), 1004-1042 (2003)
49. Piketty, T., Saez, E.: Income inequality in the united states, 1913-1998. Q. J. Econ. 118(1), 1-39 (2003)
50. Touzi, N.: Stochastic control and application to finance. Scuola Normale Superiore, Pisa. Special Research Semester on Financial Mathematics (2002)