Year: 2025
Type: article
Abstract: We propose a new mean-field game model with two states to study synchronization phenomena, and we provide a comprehensive characterization of stationary and dynamic equilibria along with their stability properties. The game undergoes a phase transition with increasing interaction strength. In the subcritical regime, the uniform distribution, representing incoherence, is the unique and stable stationary equilibrium. Above the critical interaction threshold, the uniform equilibrium becomes unstable and there is a multiplicity of stationary equilibria that are self-organizing. Under a discounted cost, dynamic equilibria spiral around the uniform distribution before converging to the self-organizing equilibria. With an ergodic cost, however, unexpected periodic equilibria around the uniform distribution emerge. Funding: This work was supported by the National Science Foundation [Grant DMS 2406762].
Authors: Felix Höfer, H. Mete Soner
Institution: Princeton University
Language: English
Topic: Game Theory and Applications
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
Funder: National Science Foundation
Award: Mean Field Optimal Control
OpenAlex ID: W4410815431