Emergence of anti-coordinated patterns in snowdrift game by reinforcement learning

• DOI: 10.1016/j.chaos.2024.114971
• Publication Date: 2024-05-15T17:25:44Z
• Authors: Zhen-Wei Ding; Ji-Qiang Zhang; Guo-Zhong Zheng; Wei-Ran Cai; Chao-Ran Cai; Li Chen; Xu-Ming Wang
• Keywords: 0301 basic medicine; Physics - Physics and Society; 03 medical and health sciences; FOS: Physical sciences; Physics and Society (physics.soc-ph)

Patterns by self-organization in nature have garnered significant interest in a range of disciplines due to their intriguing structures. In the context of the snowdrift game (SDG), which is considered as an anti-coordination game, but the anti-coordination patterns are counterintuitively rare. In the work, we introduce a model called the Two-Agents, Two-Action Reinforcement Learning Evolutionary Game ($2\times 2$ RLEG), and apply it to the SDG on regular lattices. We uncover intriguing phenomena in the form of Anti-Coordinated domains (AC-domains), where different frustration regions are observed and continuous phase transitions at the boundaries are identified. To understand the underlying mechanism, we develop a perturbation theory to analyze the stability of different AC-domains. Our theory accurately partitions the parameter space into non-anti-coordinated, anti-coordinated, and mixed areas, and captures their dependence on the learning parameters. Lastly, abnormal scenarios with a large learning rate and a large discount factor that deviate from the theory are investigated by examining the growth and nucleation of AC-domains. Our work provides insights into the emergence of spatial patterns in nature, and contributes to the development of theory for analysing their structural complexities.