Evolution of cooperation on dynamical asymmetrical networks with costs

Abstract Social networks denote the structure of interactions among individuals. Adjusting social relationships is a typical reaction among humans attempting to interact with altruistic partners. Theoretical investigations proved that dynamical network structures promote the evolution of cooperation. However, individuals react differently to diverse social partners and interactions. Furthermore, a large variety of potential costs of partner switching occur in real-world interactions. Establishing and maintaining different interactions cost differently. Based on these motivations, this investigation studies the interplay between the dynamics on networks and the dynamics of networks, which entangles the evolution of strategies and topology of adaptive multilayer networks whose structure is divided into a gaming layer for reaping payoff and a learning layer for spreading strategy. Individuals react differently to overlapped and un-overlapped partners whose gaming interactions and learning interactions are identical or not. And the effects of overlap levels and rewiring costs on the evolution of cooperation are explored. Simulation results demonstrate that increasing the ratio of rewiring as well as the overlap levels can enhance the evolution of cooperation significantly. However, both too frequent rewiring and too high overlap levels can result in the increment of isolated nodes, and thus provide a sanctuary for defectors to survive and make cooperators hardly to occupy the whole population. Moreover, it is found that rewiring costs have dramatically different impacts on the evolution of cooperation for different overlap levels. For a low overlap level, increasing costs suppress the evolution of cooperation. Yet a high overlap level makes increasing costs favor the cooperator to spread. Our results reveal the condition for the domination of cooperation with asymmetrical interactions, which may provide a potential way to understand the evolutionary cooperation in human society.