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

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.