Evolutionary prisoner''s dilemma on Newman--Watts socialnetworks with an asymmetric payoff distribution mechanism

In this paper, we introduce an asymmetric payoff distribution mechanism into the evolutionary prisoner's dilemma game (PDG) on Newman--Watts social networks, and study its effects on the evolution of cooperation. The asymmetric payoff distribution mechanism can be adjusted by the parameter $\alpha$: if $\alpha>0$, the rich will exploit the poor to get richer; if $\alpha<0$, the rich are forced to offer part of their income to the poor. Numerical results show that the cooperator frequency monotonously increases with $\alpha$ and is remarkably promoted when $\alpha>0$. The effects of updating order and self-interaction are also investigated. The co-action of random updating and self-interaction can induce the highest cooperation level. Moreover, we employ the Gini coefficient to investigate the effect of asymmetric payoff distribution on the the system's wealth distribution. This work may be helpful for understanding cooperative behaviour and wealth inequality in society.