Synchronization Games
提出一个两状态平均场博弈模型来研究同步现象，刻画了平稳和动态均衡及其稳定性，发现随交互强度增加系统从无序到自组织均衡的相变。
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].