A mean field game model with non-local spatial interactions and resources accumulation

TL;DR

This paper introduces a novel mean field game model with non-local spatial interactions and resource accumulation, addressing less regular data and state constraints, and establishes the existence of solutions for this complex PDE system.

Contribution

It develops a new mean field game framework incorporating non-local interactions and resource dynamics, extending existing models to less regular settings and proving solution existence.

Findings

Established existence of solutions for the PDE system

Extended mean field game models to include resource accumulation

Addressed regularity and state constraint challenges

Abstract

We study a family of mean field games arising in modeling the behavior of strategic economic agents which move across space maximizing their utility from consumption and have the possibility to accumulate resources for production (such as human capital). The resulting mean field game PDE system is not covered in the actual literature on the topic as it displays weaker assumptions on the regularity of the data (in particular global Lipschitz continuity and boundedness of the objective are lost), state constraints, and a non-standard interaction term. We obtain a first result on the existence of solution of the mean field game PDE system.