  We study the evolution of cooperation in a finite population interacting
according to a simple model of like-with-like assortment. Evolution proceeds as
a Moran process, and payoffs from the underlying cooperator-defector game are
translated to positive fitnesses by an exponential transformation. These
evolutionary dynamics can arise, for example, in a nest-structured population
with rare migration. The use of the exponential transformation, rather than the
usual linear one, is appropriate when interactions have multiplicative fitness
effects, and allows for a tractable characterization of the effect of
assortment on the evolution of cooperation. We define two senses in which a
greater degree of assortment can favour the evolution of cooperation, the first
stronger than the second: (i) greater assortment increases, at all population
states, the probability that the number of cooperators increases, relative to
the probability that the number of defectors increases; and (ii) greater
assortment increases the fixation probability of cooperation, relative to that
of defection. We show that, by the stronger definition, greater assortment
favours 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 favours
cooperation by the weak definition, but not by the strong definition. Our
results hold for any strength of selection.
