Group-size effects on the evolution of cooperation in the spatial public goods game

TL;DR

This study investigates how varying group sizes in spatial public goods games influence cooperation, revealing that larger groups can enhance cooperation through spatial reciprocity, but also enable defectors to exploit distant players.

Contribution

It demonstrates that increasing group size promotes cooperation via spatial reciprocity and payoff collection methods, challenging traditional mean-field assumptions.

Findings

Larger groups can promote cooperation through spatial reciprocity.

Small numbers of defectors are tolerable in large groups, expanding mixed phases.

Distant payoff collection allows defectors to invade cooperators.

Abstract

We study the evolution of cooperation in public goods games on the square lattice, focusing on the effects that are brought about by different sizes of groups where individuals collect their payoffs and search for potential strategy donors. We find that increasing the group size does not necessarily lead to mean-field behavior, as is traditionally observed for games governed by pairwise interactions, but rather that public cooperation may be additionally promoted by means of enhanced spatial reciprocity that sets in for very large groups. Our results highlight that the promotion of cooperation due to spatial interactions is not rooted solely in having restricted connections amongst players, but also in individuals having the opportunity to collect payoffs separately from their direct opponents. Moreover, in large groups the presence of a small number of defectors is bearable, which makes the mixed phase region expand with increasing group size. Having a chance of exploiting distant players, however, offers defectors a new way to break the phalanx of cooperators, and even to resurrect from small numbers to eventually completely invade the population.