Evolutionary dynamics in division of labor games on cycle networks

Abstract

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.