Synchronization Games
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911995160166400 |
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| author | Höfer, Felix Soner, H. Mete |
| author_facet | Höfer, Felix Soner, H. Mete |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08842 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Synchronization Games Höfer, Felix Soner, H. Mete Optimization and Control 34C25, 34H05, 37G35, 49L20, 91A16, 92B25 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. |
| title | Synchronization Games |
| topic | Optimization and Control 34C25, 34H05, 37G35, 49L20, 91A16, 92B25 |
| url | https://arxiv.org/abs/2402.08842 |