Depreciation of public goods in spatial public goods games

Abstract

In real situations, the value of public goods will be reduced or even lost because of externalfactors or for intrinsic reasons. In this work, we investigate the evolution of cooperation byconsidering the effect of depreciation of public goods in spatial public goods games on a squarelattice. It is assumed that each individual gains full advantage if the number of the cooperatorsnc within a group centered on that individual equals or exceeds the critical mass (CM).Otherwise, there is depreciation of the public goods, which is realized by rescaling the multiplicationfactor r to (nc/CM)r. It is shown that the emergence of cooperation is remarkably promoted forCM > 1 even at smallvalues of r, and a global cooperative level is achieved at an intermediate value ofCM = 4 at asmall r. We further study the effect of depreciation of public goods on different topologies of a regularlattice, and find that the system always reaches global cooperation at a moderate value ofCM = G − 1 regardless of whether or not there exist overlapping triangle structures on the regular lattice, whereG is the group size of the associated regular lattice.