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.
Highlights
The stability of modern human societies relies on public goods that future generations have, for many decades past, increasingly often taken for granted [1]
Instead of the application of a single level of tolerance [54], the question is whether diverse tolerance strategies offer evolutionary advantages over default abstinence, and whether there is synergy or competition among them? As we will show, advantages to tolerance and synergies do exist, such that players with a different threshold in terms of the tolerated number of defectors in a group provide an optimal response to the public goods dilemma
The behavior of tolerant players depends sensitively on the number of defectors within a group, which we denote as nD
Summary
The stability of modern human societies relies on public goods that future generations have, for many decades past, increasingly often taken for granted [1]. Advantages to tolerance and synergies do exist, such that players with a different threshold in terms of the tolerated number of defectors in a group provide an optimal response to the public goods dilemma These solutions are made possible by the spontaneous emergence of complex spatial patterns that require a sufficiently large system size to emerge from random initial conditions. We will show that some globally stable subsystem solutions remain completely invisible even at a large system size, which is a striking manifestation of the subtleties that self-organising processes in a complex system may evoke Before presenting these results in more detail, we first proceed with the description of the public goods game with diverse levels of tolerance
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