Cooperative behavior in a spatial model of "commons"

TL;DR

This paper models a spatial 'commons' system where local sharing and agent interactions lead to complex, critical patterns with dominant altruists and fluctuating dynamics, revealing a power-law behavior in activity fluctuations.

Contribution

It introduces a lattice model of commons with local sharing, analyzing its critical behavior and fluctuation dynamics under different mutation rates.

Findings

Steady state dominated by altruist agents with complex patterns.

Power spectrum of activity fluctuations follows a 1/f^α behavior with α ~ 1.30.

Slow mutation rates promote higher cooperative tendencies through slow fluctuations.

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 $1/f^\alpha$ behavior with $\alpha \sim 1.30$. In case of very slow mutation rate the steady state has slow fluctuations which helps the evolution of higher cooperative tendency.