Emergence of moving pattern in a collective game

[摘要] In this paper, we propose a collective game where agents, distributed in one-dimensional space, seek for their best positions through adaptive learning. The movements of agents are driven by a simple rule: they are attracted by others with higher status and yet restricted by their initial positions, according to which a benefit function is formulated. It is found that some fascinating complex patterns arise from such simple rules. Aggregations of agents emerge in the form of clusters along this position line after a dozen rounds. While agents strive to move forward, a chain of clusters shift backward and ultimately collapse one by one at an almost fixed point. The trail of shifting behaves like an attractor which attracts different groups of agents to join in. Such intricate moving pattern turns out quite sharp and clear when agents have a uniform pace length.

[发布机构] School of Systems Science, Beijing Normal University, Beijing; 100875, China^1

[效力级别] 数学

[关键词] Adaptive learning;Benefit functions;Best position;Complex pattern;Fixed points