Existence and Uniqueness of Solutions for Bertrand and Cournot Mean Field Games

We study a system of partial differential equations used to describe Bertrand and Cournot competition among a continuum of producers of an exhaustible resource. By deriving new a priori estimates, we prove the existence of classical solutions under general assumptions on the data. Moreover, under an...

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Veröffentlicht in:	Applied mathematics & optimization 2018-02, Vol.77 (1), p.47-71
Hauptverfasser:	Graber, P. Jameson, Bensoussan, Alain
Format:	Artikel
Sprache:	eng
Schlagworte:	Calculus of Variations and Optimal Control Optimization CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS Control Economic analysis Economic models FOKKER-PLANCK EQUATION Game theory HAMILTON-JACOBI EQUATIONS Mathematical and Computational Physics Mathematical Methods in Physics MATHEMATICAL SOLUTIONS Mathematics Mathematics and Statistics MEAN-FIELD THEORY Numerical and Computational Physics OPTIMAL CONTROL Partial differential equations Simulation Systems Theory Theoretical Uniqueness
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Beschreibung
Zusammenfassung:	We study a system of partial differential equations used to describe Bertrand and Cournot competition among a continuum of producers of an exhaustible resource. By deriving new a priori estimates, we prove the existence of classical solutions under general assumptions on the data. Moreover, under an additional hypothesis we prove uniqueness.
ISSN:	0095-4616 1432-0606
DOI:	10.1007/s00245-016-9366-0