Abstract
Evolutionary games provide a flexible mathematical framework for many problems in biology and social evolution. Prisoners' dilemma, and in particular, the important special case of donation games, represents social dilemmas where cooperation is mutually beneficial, yet defection is preferred by selfish agents. In evolutionary games on networks, the agents interact over a population structure. The existence of population structures that promote cooperative behavior is a fascinating and active research topic. Previous research establishes structures promoting cooperation in the limit of weak selection where the benefit-to-cost ratio β exceeds 1.5. The existence of such structures for medium and strong selection for [Formula: see text] and for weak selection for [Formula: see text] has been a long-standing open question. First, we answer the open questions in the affirmative: For every selection strength and every [Formula: see text], we construct networks promoting cooperation. Second, we present a robustness result with respect to β and selection strength: Our structures promote cooperation for a range of these parameter values rather than specific parameter values. Finally, we supplement our theoretical results with simulation results on small population structures that show the effectiveness of our construction over well-studied population structures.