Cooperative behavior in a spatial model of "commons"

Abstract

We study a lattice model of ``commons'', where a resource is shared locally among the agents of various cooperative tendency. The payoff function of an agent is proportional to the fraction of his operation rate and the net output of the resource. After each time step a site is occupied by the neighbor of maximum profit or by its owner himself. In steady state the model is dominated by ``altruist'' agents with a small minority of selfish agents, forming a complex pattern. The dynamics selects cooperative levels in a way that the model becomes critical. We study the critical behavior of the model in case of moderate mutation rate and find the power spectrum of fluctuation of activity shows a $1/f^α$ behavior with $α\sim 1.30$. In case of very slow mutation rate the steady state has slow fluctuations which helps the evolution of higher cooperative tendency.