  Studies of cooperation have traditionally focused on discrete games such as
the well-known prisoner's dilemma, in which players choose between two pure
strategies: cooperation and defection. Increasingly, however, cooperation is
being studied in continuous games that feature a continuum of strategies
determining the level of cooperative investment. For the continuous snowdrift
game, it has been shown that a gradually evolving monomorphic population may
undergo evolutionary branching, resulting in the emergence of a defector
strategy that coexists with a cooperator strategy. This phenomenon has been
dubbed the 'tragedy of the commune'. Here we study the effects of fluctuating
group size on the tragedy of the commune and derive analytical conditions for
evolutionary branching. Our results show that the effects of fluctuating group
size on evolutionary dynamics critically depend on the structure of payoff
functions. For games with additively separable benefits and costs, fluctuations
in group size make evolutionary branching less likely, and sufficiently large
fluctuations in group size can always turn an evolutionary branching point into
a locally evolutionarily stable strategy. For games with multiplicatively
separable benefits and costs, fluctuations in group size can either prevent or
induce the tragedy of the commune. For games with general interactions between
benefits and costs, we derive a general classification scheme based on second
derivatives of the payoff function, to elucidate when fluctuations in group
size help or hinder cooperation.
