Variability in group size and the evolution of collective action

Models of the evolution of collective action typically assume that interactions occur in groups of identical size. In contrast, social interactions between animals occur in groups of widely dispersed size. This paper models collective action problems as two-strategy multiplayer games and studies the effect of variability in group size on the evolution of cooperative behavior under the replicator dynamics. The analysis identifies elementary conditions on the payoff structure of the game implying that the evolution of cooperative behavior is promoted or inhibited when the group size experienced by a focal player is more or less variable. Similar but more stringent conditions are applicable when the confounding effect of size-biased sampling, which causes the group-size distribution experienced by a focal player to differ from the statistical distribution of group sizes, is taken into account.