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We study the evolution of cooperation in a finite population interactingaccording to a simple model of like-with-like assortment. Evolution proceeds asa Moran process, and payoffs from the underlying cooperator-defector game aretranslated to positive fitnesses by an exponential transformation. Theseevolutionary dynamics can arise, for example, in a nest-structured populationwith rare migration. The use of the exponential transformation, rather than theusual linear one, is appropriate when interactions have multiplicative fitnesseffects, and allows for a tractable characterization of the effect ofassortment on the evolution of cooperation. We define two senses in which agreater degree of assortment can favour the evolution of cooperation, the firststronger than the second: (i) greater assortment increases, at all populationstates, the probability that the number of cooperators increases, relative tothe probability that the number of defectors increases; and (ii) greaterassortment increases the fixation probability of cooperation, relative to thatof defection. We show that, by the stronger definition, greater assortmentfavours the evolution of cooperation for a subset of cooperative dilemmas:prisoners' dilemmas, snowdrift games, stag-hunt games, and some prisoners'delight games. For other cooperative dilemmas, greater assortment favourscooperation by the weak definition, but not by the strong definition. Ourresults hold for any strength of selection.

Assortment and the evolution of cooperation in a Moran process with exponential fitness