Dynamics of asymmetric division of labor game with environmental feedback

This paper investigates asymmetric division of labor game with environmental feedback, in which players have innate returns provided by rich patch and nothing by poor patch. An imitative dynamical model is proposed and some sufficient conditions for stability of equilibria are derived. The conditions of stability depend exclusively on costs of strategies, benefit of cooperation and weighted benefit of player in rich patch. Theoretical results are supported by numerical experiments. Furthermore, the frequency of each strategy in different patches is obtained by numerical simulation.