Uniqueness of solutions to MFG systems with large discount

2025/10/10 by Cirant, Marco, Continelli, Elisa · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.09280

Abstract

We prove that solutions to a class of Mean Field Game systems with discount are unique provided that the discount factor is large enough, and the Lagrangian term is (proportionally) small enough. This identifies an asymptotic uniqueness regime that falls outside the usual ones involving monotonicity.

Citations

• The exponential turnpike phenomenon for mean field game systems: weakly monotone drifts and small interactions
• Hidden monotonicity and canonical transformations for mean field games and master equations
• On monotonicity conditions for Mean Field Games
• Mean Field Games systems under displacement monotonicity
• Well-posedness of mean field games master equations involving non-separable local Hamiltonians
• Convergence of some Mean Field Games systems to aggregation and flocking models
• On non-uniqueness in mean field games
• Weighted Energy-Dissipation principle for gradient flows in metric spaces
• On the existence of oscillating solutions in non-monotone Mean-Field Games
• Uniqueness of solutions in Mean Field Games with several populations and Neumann conditions
• On non-uniqueness and uniqueness of solutions in finite-horizon mean field games
• Time-dependent focusing Mean-Field Games: the sub-critical case
• Stable solutions in potential mean field game systems
• A review on attractive-repulsive hydrodynamics for consensus in collective behavior

Cited by

• The local Turnpike Property in Mean Field Control and Games with quadratic Hamiltonian

Related

• Weak-strong uniqueness for solutions to mean-field games
• On non-uniqueness and uniqueness of solutions in finite-horizon mean field games
• On non-uniqueness in mean field games
• A uniqueness result for finite-state mean field games with non-separable Hamiltonian
• New Uniqueness Results For A Mean Field Game Of Controls