On quasi-stationary Mean Field Games of Controls

2022/04/11 by Fabio Camilli, Camilli, Fabio, Claudio Marchi +1 · 2 citations
Decision Sciences · Economics, Econometrics and Finance · #35B40 #35Q91 #49N70 #Analysis of PDEs (math.AP) #Economic theories and models #FOS: Mathematics #Game Theory and Applications #Optimization and Control (math.OC) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2204.04947

openalex publication_date 2022/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Approximately optimal distributed controls for high-dimensional stochastic systems with pairwise interaction through controls
• Existence of Solutions and Selection Problem for Quasi-stationary Contact Mean Field Games

Related

• On quasi-stationary Mean Field Games models
• On Classical Solutions to the Mean Field Game System of Controls
• Some remarks on Mean Field Games
• Mean Field Games of Controls: Propagation of Monotonicities
• Mean Field Games of Controls: on the convergence of Nash equilibria