  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.
