  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.
