Stochastic dynamics of division of labor games in finite populations

A theoretical investigation on the strategy evolution in the self-organized division of labor dilemma is performed by means of evolutionary game theory. The often-used Fermi function is employed for driving the strategy updating, based on which the fixation probability of the involved strategy (performing which task) is calculated. Results about the evolution dynamics of the division of labor for two-player games are: (1) the fixation probabilityfor any selection intensity is derived; (2) the fixation probability and fixation time under weak selection are gained and a comparison with neutral selection is performed. In this case, the conditions to facilitate cooperation in division of labor are found. Then we extend the model to a multi-player one to describe the self-organized task allocation when multiple players are involved in one game. Relevant results for weak selection to favor the coexistence state of the two strategies for the multi-player games are gained. These results help understand and design effective mechanism where self-organized collective dynamics occurs in the form of maximizing the benefit of the multi-agent system.