Promoting cooperation by punishing minority

TL;DR

This paper introduces a punishment mechanism where majority players punish minorities in public goods games, significantly boosting cooperation levels and revealing phase transitions depending on punishment severity and multiplication factors.

Contribution

It proposes a novel punishment strategy targeting majority players punishing minorities, enhancing cooperation in public goods games, supported by theoretical and simulation analyses.

Findings

Cooperation increases with the multiplication factor under no or small punishment fines.

Large punishment fines cause a sudden jump in cooperation at a critical multiplication factor.

The study analyzes the density of different group types under the proposed mechanism.

Abstract

Punishment is an effective way to sustain cooperation among selfish individuals. In most of previous studies, objects of punishment are set to be defectors. In this paper, we propose a mechanism of punishment, in which individuals with the majority strategy will punish those with the minority strategy in a public goods game group. Both theoretical analysis and simulation show that the cooperation level can be greatly enhanced by punishing minority. For no punishment or small values of punishment fine, the fraction of cooperators continuously increases with the multiplication factor. However, for large values of punishment fine, there exists a critical value of multiplication factor, at which the fraction of cooperators suddenly jumps from 0 to 1. The density of different types of groups is also studied.