Inverse problems for mean field games

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Article number085003
Journal / PublicationInverse Problems
Volume39
Issue number8
Online published22 Jun 2023
Publication statusPublished - Aug 2023

Abstract

The theory of mean field games studies the limiting behaviors of large systems where the agents interact with each other in a certain symmetric way. The running and terminal costs are critical for the agents to decide the strategies. However, in practice they are often partially known or totally unknown for the agents, while the total cost is known at the end of the game. To address this challenging issue, we propose and study several inverse problems for mean field games. When the Lagrangian is a kinetic energy, we first establish unique identifiability results, showing that one can recover either the running cost or the terminal cost from knowledge of the total cost. If the running cost is limited to the time-independent class, we can further prove that one can simultaneously recover both the running and the terminal costs. Finally, we extend the results to the setup with general Lagrangians. © 2023 IOP Publishing Ltd

Research Area(s)

  • mean field games, inverse problems, master equation, unique identifiability

Citation Format(s)

Inverse problems for mean field games. / Liu, Hongyu; Mou, Chenchen; Zhang, Shen.
In: Inverse Problems, Vol. 39, No. 8, 085003, 08.2023.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review