  Understanding the conditions for maintaining cooperation in groups of
unrelated individuals despite the presence of non-cooperative members is a
major research topic in contemporary biological, sociological, and economic
theory. The $N$-person snowdrift game models the type of social dilemma where
cooperative actions are costly, but there is a reward for performing them. We
study this game in a scenario where players move between play groups following
the casual group dynamics, where groups grow by recruiting isolates and shrink
by losing individuals who then become isolates. This describes the size
distribution of spontaneous human groups and also the formation of sleeping
groups in monkeys. We consider three scenarios according to the probability of
isolates joining a group. We find that for appropriate choices of the
cost-benefit ratio of cooperation and the aggregation-disaggregation ratio in
the formation of casual groups, free-riders can be completely eliminated from
the population. If individuals are more attracted to large groups, we find that
cooperators persist in the population even when the mean group size diverges.
We also point out the remarkable similarity between the replicator equation
approach to public goods games and the trait group formulation of structured
demes.
