The mechanisms of labor division from the perspective of task urgency and game theory

Labor division is a prevalent phenomenon in nature, drawing the attention of researchers across various fields owing to its inherent cooperative dilemmas. The study of how groups of self-interested individuals maintain a harmonious division of labor is both fascinating and significant. However, the majority of existing game models, which are rooted in two-player interactions, often fail to accurately represent real-world scenarios where interactions between individuals are not widespread. To bridge this gap, we present the Division of Labor Game within Community (DOLC) model. This paper begins with an overview of the problem's background, progressing to the development of the DOLC mathematical model. Subsequent sections delve into theoretical analyses and simulations of the two-task variant of the DOLC, before exploring its extension to multi-task scenarios and investigating the impact of network structures on cooperative dynamics. Our research reveals critical insights: in the absence of the urgency coefficient, members of the community invariably choose the same task, hindering cooperative efforts. Conversely, the urgency coefficient positively influences the evolution of intra-group labor division, while the selection intensity tends to undermine it. These dynamics persist even in multi-task configurations of the DOLC model, and network circulation often hampers group collaboration. These findings have promising applications in enhancing the efficiency of unmanned systems and optimizing strategies for task allocation and scheduling.