Numerical Methods for Finite-State Mean-Field Games Satisfying a Monotonicity Condition

Diogo A. Gomes; João Saúde

doi:10.1007/s00245-018-9510-0

Numerical Methods for Finite-State Mean-Field Games Satisfying a Monotonicity Condition

Diogo A. Gomes^*, João Saúde

^*Corresponding author for this work

Applied Mathematics and Computational Science

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

11 Scopus citations

Abstract

Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard conditions make the numerical approximation of MFGs difficult. Using the monotonicity condition, we build a flow that is a contraction and whose fixed points solve both for stationary and time-dependent MFGs. We illustrate our methods with a MFG that models the paradigm-shift problem.

Original language	English (US)
Pages (from-to)	51-82
Number of pages	32
Journal	Applied Mathematics and Optimization
Volume	83
Issue number	1
DOIs	https://doi.org/10.1007/s00245-018-9510-0
State	Published - Feb 2021

Bibliographical note

Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

Finite state problems
Mean-field games
Monotonicity methods

ASJC Scopus subject areas

Control and Optimization
Applied Mathematics

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10.1007/s00245-018-9510-0

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abstract = "Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard conditions make the numerical approximation of MFGs difficult. Using the monotonicity condition, we build a flow that is a contraction and whose fixed points solve both for stationary and time-dependent MFGs. We illustrate our methods with a MFG that models the paradigm-shift problem.",

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AB - Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard conditions make the numerical approximation of MFGs difficult. Using the monotonicity condition, we build a flow that is a contraction and whose fixed points solve both for stationary and time-dependent MFGs. We illustrate our methods with a MFG that models the paradigm-shift problem.

KW - Finite state problems

KW - Mean-field games

KW - Monotonicity methods

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Numerical Methods for Finite-State Mean-Field Games Satisfying a Monotonicity Condition

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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