On quasi-stationary Mean Field Games of Controls

TL;DR

This paper introduces and analyzes quasi-stationary Mean Field Games of Controls, where agents choose strategies based only on current information without predicting population evolution, proving existence and uniqueness of solutions.

Contribution

It extends classical Mean Field Games of Controls by modeling agents with non-anticipative strategy choices and establishes foundational mathematical results for this new framework.

Findings

Proved existence of solutions under various conditions

Established uniqueness of solutions in the quasi-stationary setting

Provided examples fitting the theoretical framework

Abstract

In Mean Field Games of Controls, the dynamics of the single agent is influenced not only by the distribution of the agents, as in the classical theory, but also by the distribution of their optimal strategies. In this paper, we study quasi-stationary Mean Field Games of Controls, which differs from the standard case in the strategy-choice mechanism of the agent: it cannot predict the evolution of the population, but chooses its strategy only on the basis of the information available at the given instant of time, without anticipating. We prove existence and uniqueness for the solution of the corresponding quasi-stationary Mean Field Games system under different sets of hypotheses and we provide some examples of models which fall within these hypotheses.