Nonlocal Bertrand and Cournot mean field games with general nonlinear demand schedule

Autor: P. Jameson Graber, Ariel Neufeld, Vincenzo Ignazio

Publikováno v: Journal de Mathématiques Pures et Appliquées. 148:150-198

In this article we prove the existence of classical solutions to a system of mean field games arising in the study of exhaustible resource production under market competition. Individual trajectories are modeled by a controlled diffusion process with

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2a06062cde61e976f6ede1b924b8090c
https://doi.org/10.1016/j.matpur.2021.02.002

Weak solutions for potential mean field games of controls

Autor: Alan Mullenix, P. Jameson Graber, Laurent Pfeiffer

Publikováno v: Nonlinear Differential Equations and Applications
Nonlinear Differential Equations and Applications, 2021, 28 (5), Paper No 50, 34 p. ⟨10.1007/s00030-021-00712-9⟩
Nonlinear Differential Equations and Applications, Springer Verlag, 2021, 28 (5), Paper No 50, 34 p. ⟨10.1007/s00030-021-00712-9⟩

International audience; We analyze a system of partial differential equations that model a potential mean field game of controls, briefly MFGC. Such a game describes the interaction of infinitely many negligible players competing to optimize a person

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dd08a43d5b1dc304c6b51d45099a4c75
https://inria.hal.science/hal-03058249

The planning problem in mean field games as regularized mass transport

Autor: Daniela Tonon, Francisco J. Silva, P. Jameson Graber, Alpár Richárd Mészáros

Publikováno v: Calculus of variations and partial differential equations, 2019, Vol.58(3), pp.115 [Peer Reviewed Journal]

In this paper, using variational approaches, we investigate the first order planning problem arising in the theory of mean field games. We show the existence and uniqueness of weak solutions of the problem in the case of a large class of Hamiltonians

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4348ec6df02834ac241e041d7d6fce4d
https://doi.org/10.1007/s00526-019-1561-9

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

Autor: P. Jameson Graber, Alain Bensoussan

Publikováno v: Applied Mathematics & Optimization. 77:47-71

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 g

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::0b686fb015774a2b7c30c350a841048e
https://doi.org/10.1007/s00245-016-9366-0

Mixed finite elements for global tide models with nonlinear damping

Autor: Colin J. Cotter, Robert C. Kirby, P. Jameson Graber

We study mixed finite element methods for the rotating shallow water equations with linearized momentum terms but nonlinear drag. By means of an equivalent second-order formulation, we prove long-time stability of the system without energy accumulati

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fcf505df2f2217693dbf1245b66a714a
http://hdl.handle.net/10044/1/61679