Competition of tolerant strategies in the spatial public goods game

TL;DR

This paper investigates how diverse levels of tolerance among players in a spatial public goods game can promote cooperation and create complex dynamic patterns, emphasizing the importance of diversity in public goods provisioning.

Contribution

It introduces tolerant strategies with variable thresholds into the spatial public goods game, revealing their role in stabilizing cooperation and generating complex spatiotemporal patterns.

Findings

Diversity of tolerance can lead to synergistic effects that promote cooperation.

Complex pattern formation and stable strategy alliances emerge in structured populations.

Tolerance diversity influences the stability and dynamics of public goods provision.

Abstract

Tolerance implies enduring trying circumstances with a fair and objective attitude. To determine whether evolutionary advantages might be stemming from diverse levels of tolerance in a population, we study a spatial public goods game, where in addition to cooperators, defectors, and loners, tolerant players are also present. Depending on the number of defectors within a group, a tolerant player can either cooperate in or abstain from a particular instance of the game. We show that the diversity of tolerance can give rise to synergistic effects, wherein players with a different threshold in terms of the tolerated number of defectors in a group compete most effectively against defection and default abstinence. Such synergistic associations can stabilise states of full cooperation where otherwise defection would dominate. We observe complex pattern formation that gives rise to an intricate phase diagram, where invisible yet stable strategy alliances require outmost care lest they are overlooked. Our results highlight the delicate importance of diversity and tolerance for the provisioning of public goods, and they reveal fascinating subtleties of the spatiotemporal dynamics that is due to the competition of subsystem solutions in structured populations.