Effects of income redistribution on the evolution of cooperation in spatial public goods games

Income redistribution is the transfer of income from some individuals to others directly or indirectly by means of social mechanisms, such as taxation, public services and so on. Employing a spatial public goods game, we study the influence of income redistribution on the evolution of cooperation. Two kinds of evolutionary models are constructed, which describe local and global redistribution of income respectively. In the local model, players have to pay part of their income after each PGG and the accumulated income is redistributed to the members. While in the global model, all the players pay part of their income after engaging in all the local PGGs, which are centered on himself and his nearest neighbours, and the accumulated income is redistributed to the whole population. We show that the cooperation prospers significantly with increasing income expenditure proportion in the local redistribution of income, while in the global model the situation is opposite. Furthermore, the cooperation drops dramatically from the maximum curvature point of income expenditure proportion. In particular, the intermediate critical points are closely related to the renormalized enhancement factors.