From Nash to Cournot - Nash equilibria via the Monge - Kantorovich problem

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

Volumn 372, Issue 2028, 2014, Pages

  Blanchet, Adrien ^a   Carlier, Guillaume ^b  

^a UNIVERSITÉ DE TOULOUSE   (France)

^b UNIVERSITÉ PARIS DAUPHINE   (France)

Author keywords

Cournot Nash equilibria; Games with a continuum of players; Monge Kantorovich optimal transportation problem; Nash equilibria

Indexed keywords

PHILOSOPHICAL ASPECTS;

COURNOT; GAMES WITH A CONTINUUM OF PLAYERS; N-PLAYER GAMES; NASH EQUILIBRIA; OPTIMAL TRANSPORT; OPTIMAL TRANSPORTATIONS; STRATEGIC INTERACTIONS;

STATISTICAL MECHANICS;

EID: 84907870344     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2013.0398     Document Type: Article

References (18)

1. Nash JF. 1950 Equilibrium points in n-person games. Proc. Natl Acad. Sci. USA 36, 48-49. (doi:10.1073/pnas.36.1.48)
2. Aumann R. 1966 Markets with a continuum of traders. Econometrica 34, 1-17. (doi:10.2307/1909854)
3. Aumann R. 1964 Existence of competitive equilibria in markets with a continuum of traders. Econometrica 32, 39-50. (doi:10.2307/1913732)
4. 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)
5. 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)
6. Lasry J-M, Lions P-L. 2007 Mean field games. Jpn J. Math. 2, 229-260. (doi:10.1007/s11537-007-0657-8)
7. Schmeidler D. 1973 Equilibrium points of nonatomic games. J. Stat. Phys. 7, 295-300. (doi:10.1007/BF01014905)
8. Mas-Colell A. 1984 On a theorem of Schmeidler. J. Math. Econ. 3, 201-206. (doi:10.1016/0304-4068(84)90029-6)
9. Villani C. 2003 Topics in optimal transportation. Graduate Studies in Mathematics, vol. 58. Providence, RI: American Mathematical Society.
10. Villani C. 2009 Optimal transport: old and new. Grundlehren der mathematischen Wissenschaften. Berli, Germany: Springer.
11. Blanchet A, Carlier G. 2012 Optimal transport and Cournot-Nash equilibria. (http://arxiv.org/abs/1206.6571)
12. Blanchet A, Carlier G. 2014 Remarks on existence and uniqueness of Cournot-Nash equilibria in the non-potential case. (http://arxiv.org/abs/1405.1354v1)
13. Cardialaguet P. 2013 Notes on mean field games. See https://www.ceremade.dauphine.fr/cardalia/MFG20130420.pdf.
14. Ambrosio L, Gigli N, Savaré G. 2008 Gradient flows in metric spaces and in the space of probability measures, 2nd edn. Lectures in Mathematics ETH Zürich. Basel, Switzerland: Birkhäuser.
15. Jordan R, Kinderlehrer D, Otto F. 1998 The variational formulation of the Fokker-Planck equation. SIAM J. Math. Anal. 29, 1-17. (doi:10.1137/S0036141096303359)
16. Carrillo JA, DiFrancesco M, Figalli A, Laurent T, Slepčev D. 2011 Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations. Duke Math. J. 156, 229-271. (doi:10.1215/00127094-2010-211)
17. Balagué D, Carrillo JA, Laurent T, Raoul G. 2013 Dimensionality of local minimizers of the interaction energy. Arch. Ration. Mech. Anal. 209, 1055-1088. (doi:10.1007/s00205-013-0644-6)
18. Degond P, Liu J-G, Ringhofer C. 2013 Large-scale dynamics of mean-field games driven by local Nash equilibria. J. Nonlinear Sci. 24, 93-115. (doi:10.1007/s00332-013-9185-2)