Hypoelliptic mean field games – a case study

Ermal Feleqi; Diogo Gomes; Teruo Tada

Hypoelliptic mean field games – a case study

Ermal Feleqi^*, Diogo Gomes, Teruo Tada

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We study hypoelliptic mean-field games (MFG) that arise in stochastic control problems of degenerate diffusions. Here, we consider MFGs with quadratic Hamiltonians and prove the existence and uniqueness of solutions. Our main tool is the Hopf-Cole transform that converts the MFG into an eigenvalue problem. We prove the existence of a principal eigenvalue and a positive eigenfunction, which are then used to construct the unique solution to the original MFG.

Original language	English (US)
Pages (from-to)	305-326
Number of pages	22
Journal	Minimax Theory and its Applications
Volume	5
Issue number	2
State	Published - 2020

Bibliographical note

Publisher Copyright:
© 2020, Heldermann Verlag. All rights reserved.

Keywords

Eigenvalue problems
Hypoelliptic operator
Mean-Field Games
Stationary problems

ASJC Scopus subject areas

Analysis
Control and Optimization
Computational Mathematics

Cite this

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abstract = "We study hypoelliptic mean-field games (MFG) that arise in stochastic control problems of degenerate diffusions. Here, we consider MFGs with quadratic Hamiltonians and prove the existence and uniqueness of solutions. Our main tool is the Hopf-Cole transform that converts the MFG into an eigenvalue problem. We prove the existence of a principal eigenvalue and a positive eigenfunction, which are then used to construct the unique solution to the original MFG.",

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AU - Feleqi, Ermal

AU - Gomes, Diogo

AU - Tada, Teruo

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N2 - We study hypoelliptic mean-field games (MFG) that arise in stochastic control problems of degenerate diffusions. Here, we consider MFGs with quadratic Hamiltonians and prove the existence and uniqueness of solutions. Our main tool is the Hopf-Cole transform that converts the MFG into an eigenvalue problem. We prove the existence of a principal eigenvalue and a positive eigenfunction, which are then used to construct the unique solution to the original MFG.

AB - We study hypoelliptic mean-field games (MFG) that arise in stochastic control problems of degenerate diffusions. Here, we consider MFGs with quadratic Hamiltonians and prove the existence and uniqueness of solutions. Our main tool is the Hopf-Cole transform that converts the MFG into an eigenvalue problem. We prove the existence of a principal eigenvalue and a positive eigenfunction, which are then used to construct the unique solution to the original MFG.

KW - Eigenvalue problems

KW - Hypoelliptic operator

KW - Mean-Field Games

KW - Stationary problems

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M3 - Article

AN - SCOPUS:85105296568

SN - 2199-1413

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SP - 305

EP - 326

JO - Minimax Theory and its Applications

JF - Minimax Theory and its Applications

IS - 2

ER -

Hypoelliptic mean field games – a case study

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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