Stable solutions in potential mean field game systems

2016/12/06 by Ariela Briani, Briani, Ariela, Pierre Cardaliaguet +1 · 6 citations
Computer Science · Decision Sciences · Economics, Econometrics and Finance · #Adaptive Dynamic Programming Control #FOS: Mathematics #Game Theory and Applications #Optimization and Control (math.OC) #Stochastic processes and financial applications

paper · doi:10.48550/arxiv.1612.01877

openalex publication_date 2016/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the notion of stable solution in mean field game theory: they are locally isolated solutions of the mean field game system. We prove that such solutions exist in potential mean field games and are local attractors for learning procedures.

Cited by

• The local Turnpike Property in Mean Field Control and Games with quadratic Hamiltonian
• Some error estimates for semidiscrete finite element approximations of stable solutions to mean field game systems
• On Mean-field Singular Stochastic Control Problems
• Uniqueness of solutions to MFG systems with large discount
• Singular Perturbations of Hamilton-Jacobi Equations in the Wasserstein Space
• Iterative Schemes for Markov Perfect Equilibria

Related

• Approximation and perturbations of stable solutions to a stationary mean field game system
• Remarks on potential mean field games
• Mean field games under invariance conditions for the state space
• One-dimensional stationary mean-field games with local coupling
• Learning in Mean Field Games: the Fictitious Play