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. This allows us to offer a general classification of games, elucidating when fluctuating group size helps or hinders cooperation.
Brännström, A., Gross, T., Blasius, B., & Dieckmann, U. (2011). Consequences of fluctuating group size for the evolution of cooperation. Journal of Mathematical Biology, 63, 263 - 281. https://doi.org/10.1007/s00285-010-0367-3