title: Decelerated invasion and waning-moon patterns in public goods games with delayed distribution.
abstract: We study the evolution of cooperation in the spatial public goods game, focusing on the effects that are brought about by the delayed distribution of goods that accumulate in groups due to the continuous investments of cooperators. We find that intermediate delays enhance network reciprocity because of a decelerated invasion of defectors, who are unable to reap the same high short-term benefits as they do in the absence of delayed distribution. Long delays, however, introduce a risk because the large accumulated wealth might fall into the wrong hands. Indeed, as soon as the curvature of a cooperative cluster turns negative, the engulfed defectors can collect the heritage of many generations of cooperators and by doing so start a waning-moon pattern that nullifies the benefits of decelerated invasion. Accidental meeting points of growing cooperative clusters may also act as triggers for the waning-moon effect, thus linking the success of cooperators with their propensity to fail in a rather bizarre way. Our results highlight that "investing in the future" is a good idea only if that future is sufficiently near and not likely to be burdened by inflation.
authors.affiliation: Institute of Technical Physics and Materials Science, Research Centre for Natural Sciences, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary.
authors.forename: Attila
authors.initials: A
authors.lastname: Szolnoki
authors.forename: Matjaž
authors.initials: M
authors.lastname: Perc
mesh_terms: D003198:Computer Simulation; D003299:Cooperative Behavior; D003657:Decision Making; D005716:Game Theory; D007449:Investments; D018803:Models, Economic; D008962:Models, Theoretical; D016081:Moon