Effect of self-organized interdependence between populations on the evolution of cooperation

In this article, based on interdependent networks, the effect of self-organized interdependence on the evolution of cooperation is studied. Different from the previous works, the interdependent strength, which can effectively improve the fitness of players, is taken as a kind of limited resources and co-evolves with players' strategy. We show that the self-organization of interdependent strength would spontaneously lead to power law distribution at the stationary state, where the level of cooperation in system can be significantly promoted. Furthermore, when intermediate quantity of interdependence resources existing in system, the power law distribution is most evident with the power β ≈ 1.72, meanwhile the level of cooperation also reaches the maximum value. We discuss the related microscopic system properties which are responsible for the observed results and also demonstrate that the power law distribution of interdependence resources is an elementary property which is robust against the governing repeated games and the initial resources allocation patterns.