Utility Evaluation Based on One-To-N Mapping in the Prisoner's Dilemma Game for Interdependent Networks

In the field of evolutionary game theory, network reciprocity has become an important means to promote the level of promotion within the population system. Recently, the interdependency provides a novel perspective to understand the widespread cooperation behavior in many real-world systems. In previous works, interdependency is often built from the direct or indirect connections between two networks through the one-to-one mapping mode. However, under many realistic scenarios, players may need much more information from many neighboring agents so as to make a more rational decision. Thus, beyond the one-to-one mapping mode, we investigate the cooperation behavior on two interdependent lattices, in which the utility evaluation of a focal player on one lattice may not only concern himself, but also integrate the payoff information of several corresponding players on the other lattice. Large quantities of simulations indicate that the cooperation can be substantially promoted when compared to the traditionally spatial lattices. The cluster formation and phase transition are also analyzed in order to explore the role of interdependent utility coupling in the collective cooperation. Current results are beneficial to deeply understand various mechanisms to foster the cooperation exhibited inside natural, social and engineering systems.