Mean field games systems of first order
By Pierre Cardaliaguet, P. J. Graber. 2014
156 citations recorded by the source corpus.
We consider a system of mean field games with local coupling in the deterministic limit. Under general structure conditions on the Hamiltonian and coupling, we prove existence and uniqueness of the weak solution, characterizing this solution as the minimizer of some optimal control of Hamilton-Jacobi and continuity equations. We also prove that this solution converges in the long time average to the solution of the associated ergodic problem.
Subfields: Applied Mathematics, Finance
View Paper: https://www.semanticscholar.org/paper/efa653851fd67392ce8d77ae55d27e30de980df0
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In Applied Mathematics
- Marco Cirant
- Alain Bensoussan
- P. J. Graber
- Martino Bardi
- Ermal Feleqi
- Giuseppe Mingione
- Edgard A. Pimentel
- Vardan K. Voskanyan
In Finance
- P. J. Graber
- Marco Cirant
- Alain Bensoussan
- Daniel Lacker
- Martino Bardi
- Ermal Feleqi
- Pierre Cardaliaguet
- René A. Carmona
Citations in the corpus
- Existence and Uniqueness of Solutions for Bertrand and Cournot Mean Field Games (2015, background): “There have been a number of existence and uniqueness theorems proved when V [m] depends on m both locally [23, 5, 4, 8, 7, 14, 15] and non-locally [6].”
- Stationary focusing mean-field games (2016, background): “We stress that in our case the lack of increasing monotonicity of −f cuts off from a large class of general approaches that have been developed in the MFG literature, for example in [7, 36, 15].”
- Linear Quadratic Mean Field Type Control and Mean Field Games with Common Noise, with Application to Production of an Exhaustible Resource (2016, background): “Many researchers have used this insight to generate results concerning existence and uniqueness [15, 17, 18, 53, 19] as well as computation of mean field Nash equilibria [7].”