Donation of richer individual can support cooperation in spatial voluntary prisoner's dilemma game

The compassionate behavior is present throughout the human society, and rich people always could not help having sympathy for poor individual. Inspired by this fact, we consider a donation model to describe the emergency and maintenance of cooperation with voluntary participate in spatial prisoner's dilemma game and we study this model on a square lattice. In detail, when the focal player has the least income in the group which includes his nearest four neighbors and himself, one of his neighbors who has the highest income will donate some proportion of his extra money to him. On the other hand, if focal individual is not the poorest, he will donate some incomes to his poorest neighbor. Through numeric simulation, we conclude that our donation model can promote the evolution of cooperation monotonously. Especially, the larger proportion payoff rich people can contribute, the higher level of cooperation we can get.