The evolutionary prisoner's dilemma game considering behavior interaction in a two-layered network

The multilayer networks are often a significantly more apt description of real-life systems, and considering that an individual's strategic choice can be influenced by the interaction between individuals and the individual's access to information in different channels, we explore the evolutionary prisoner's dilemma (PD) game in a two-layered network. The numerical simulation results show that when both of the two layers networks are heterogeneous networks, it is more beneficial to promote cooperation. However, it takes a longer time for the whole system to reach the stable state. In addition, with the increase of the temptation gain and the proportion of players whose behaviors may be directly affected by their counterparts, the final density of cooperators in the entire system gradually decreases. For the individuals whose behaviors may be directly affected by their counterparts, however, if they preferred to follow their neighbors' strategies, it could be conducive to promote the individuals' cooperation behavior.