This paper theoretically investigates the evolutionary dynamics in the division of labor games performed on the cycle networks. Several typical updating processes based on the Moran process are considered here: Birth-Death (BD) updating process, Death-Birth (DB) updating process and the mixed DB-BD updating process. The exponential payoff-to-fitness mapping is adopted, and analytical results for fixation time and fixation probability under the condition of strong selection are provided. In addition, numerical values of several crucial quantities within the framework of different game scenarios, decided by the payoff matrix of the division of labor (DOL) games, are studied for comparison. The conclusion clearly shows that, even under different kinds of DOL games, the fixation times are closely associated with the specific update mechanism. This work provides a deeper look into the strategic interactions and network dynamics in the context of the DOL games based on self-organized task allocation.

本文从理论上研究了在循环网络上进行的劳动博弈划分中的演化动力学。这里考虑基于Moran流程的几种典型更新流程：出生（BD）更新过程，出生（DB）更新过程和混合DB-BD更新过程。采用指数拟合指数拟合，给出强选择条件下注视时间和注视概率的分析结果。此外，还研究了由分工（DOL）游戏的收益矩阵决定的，在不同游戏场景的框架内几个关键量的数值，以进行比较。结论清楚地表明，即使在不同种类的DOL游戏中，注视时间也与特定的更新机制密切相关。