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 |
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| container_title | Applied mathematics & optimization |
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| creator | Graber, P. Jameson Bensoussan, Alain |
| description | 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. |
| doi_str_mv | 10.1007/s00245-016-9366-0 |
| format | Article |
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| source | SpringerNature Journals; EBSCOhost Business Source Complete |
| subjects | 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 |
| title | Existence and Uniqueness of Solutions for Bertrand and Cournot Mean Field Games |
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