Phase transitions and volunteering in spatial public goods games

TL;DR

This paper investigates how voluntary participation in spatial public goods games creates cyclic dominance among strategies, leading to complex patterns and phase transitions that influence cooperation and selfish behavior.

Contribution

It introduces a simple mechanism of voluntary participation that results in cyclic dominance and phase transitions in spatial public goods games, revealing new dynamical behaviors.

Findings

Voluntary participation induces cyclic dominance among strategies.

Transitions between different strategy states depend on the value of the public good.

Volunteering prevents the spread of selfish behavior and sustains cooperation.

Abstract

Cooperative behavior among unrelated individuals in human and animal societies represents a most intriguing puzzle to scientists in various disciplines. Here we present a simple yet effective mechanism promoting cooperation under full anonymity by allowing for voluntary participation in public goods games. This natural extension leads to rock--scissors--paper type cyclic dominance of the three strategies cooperate, defect and loner i.e. those unwilling to participate in the public enterprise. In spatial settings with players arranged on a regular lattice this results in interesting dynamical properties and intriguing spatio-temporal patterns. In particular, variations of the value of the public good leads to transitions between one-, two- and three-strategy states which are either in the class of directed percolation or show interesting analogies to Ising-type models. Although volunteering is incapable of stabilizing cooperation, it efficiently prevents successful spreading of selfish behavior and enables cooperators to persist at substantial levels.