Coupled dynamics of mobility and pattern formation in optional public goods games

TL;DR

This paper investigates how population density and individual mobility influence cooperation in optional public goods games, revealing conditions that promote or suppress cooperation through coevolutionary dynamics and theoretical analysis.

Contribution

It introduces a model combining population density and mobility into spatial public goods games, analyzing their effects on cooperation stability and dynamics.

Findings

Low density and slow movement favor cooperation.

Higher density and faster movement suppress cooperation.

A log-log relation exists between cooperation levels and mobility.

Abstract

In a static environment, optional participation and a local agglomeration of cooperators are found to be beneficial for the occurrence and maintenance of cooperation. In the optional public goods game, the rock-scissors-paper cycles of different strategies yield oscillatory cooperation but not stable cooperation. In this paper, by incorporating population density and individual mobility into the spatial optional public goods game, we study the coevolutionary dynamics of strategy updating and benefit-seeking migration. With low population density and slow movement, an optimal level of cooperation is easy to be reached. An increase in population density and speed-up of free-floating of competitive agents will suppress cooperation. A log-log relation between the levels of cooperation and the free-floating probability is found. Theoretical analysis indicates that the decrease of cooperator frequency in the present model should result from the increased interactions between different agents, which may originate from the increased cluster size or the speed-up of random-movement.