Evolutionary games with facilitators: When does selection favor cooperation?

TL;DR

This paper investigates how cooperation can be favored in evolutionary games with facilitators, identifying conditions under which facilitators promote the spread and replacement of cooperation in social dilemma scenarios.

Contribution

It introduces a model analyzing the role of fixed facilitators in promoting cooperation, providing conditions for when selection favors cooperation in various social dilemma games.

Findings

Facilitators increase the probability of cooperation fixation.

Critical facilitator density depends on population size and selection strength.

Cooperation can replace defection more likely under certain facilitator conditions.

Abstract

We study the combined influence of selection and random fluctuations on the evolutionary dynamics of two-strategy ("cooperation" and "defection") games in populations comprising cooperation facilitators. The latter are individuals that support cooperation by enhancing the reproductive potential of cooperators relative to the fitness of defectors. By computing the fixation probability of a single cooperator in finite and well-mixed populations that include a fixed number of facilitators, and by using mean field analysis, we determine when selection promotes cooperation in the important classes of prisoner's dilemma, snowdrift and stag-hunt games. In particular, we identify the circumstances under which selection favors the replacement and invasion of defection by cooperation. Our findings, corroborated by stochastic simulations, show that the spread of cooperation can be promoted through various scenarios when the density of facilitators exceeds a critical value whose dependence on the population size and selection strength is analyzed. We also determine under which conditions cooperation is more likely to replace defection than vice versa. Keywords: Evolutionary games; dynamics of cooperation; social dilemmas; fixation; population dynamics.