Mean Field Games with monotonous interactions through the law of states and controls of the agents

TL;DR

This paper studies a class of Mean Field Games where agents interact via the distribution of their states and controls, proving existence and uniqueness of solutions under monotonicity and growth conditions.

Contribution

It introduces a framework for Mean Field Games with interactions through states and controls, establishing existence and uniqueness results under new monotonicity assumptions.

Findings

Existence of solutions under specified conditions

Uniqueness of solutions proved using a priori estimates

Applications demonstrating the theoretical results

Abstract

We consider a class of Mean Field Games in which the agents may interact through the statistical distribution of their states and controls. It is supposed that the Hamiltonian behaves like a power of its arguments as they tend to infinity, with an exponent larger than one. A monotonicity assumption is also made. Existence and uniqueness are proved using a priori estimates which stem from the monotonicity assumptions and Leray-Schauder theorem. Applications of the results are given.