In this work, the depreciation effect of public goods is considered in the public goods games, which is realized by rescaling the multiplication factor r of each group as ~(r′)=r(~(nc)G)β (β<0). It is assumed that each individual enjoys the full profit r of the public goods if all the players of this group are cooperators. Otherwise, the value of public goods is reduced to ~(r′). It is found that compared with the original version (β=0), the emergence of cooperation is remarkably promoted for β>0, and there exist intermediate values of β inducing the best cooperation. Particularly, there exists a range of β inducing the highest cooperative level, and this range of β broadens as r increases. It is further presented that the variation of cooperator density with noise has close relations with the values of β and r, and cooperation at an intermediate value of β=1.0 is most tolerant to noise.
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