Mean-field games with unbounded controls: a weak formulation approach to global solutions

TL;DR

This paper proves the existence of equilibria in a broad class of non-Markovian mean-field games with unbounded controls using a novel weak formulation approach, extending previous results to more general settings.

Contribution

It introduces a new method for establishing equilibrium existence in mean-field games with unbounded controls, avoiding boundedness assumptions on parameters and time horizons.

Findings

Existence of equilibrium for non-Markovian mean-field games with unbounded controls.

Development of new stability results for quadratic-growth McKean-Vlasov BSDEs.

Applicable to models with quadratic running costs in control variables.

Abstract

We establish an existence of equilibrium result for a class of non-Markovian mean-field games with unbounded control space in weak formulation. Our result is based on new existence and stability results for quadratic-growth generalized McKean-Vlasov BSDEs. Unlike earlier approaches, our approach does not require boundedness assumptions on the model parameters or time horizons and allows for running costs that are quadratic in the control variable.