How the size of social groups affects the evolution of cooperative behaviors is a classic question in evolutionary biology. Here we investigate group size effects in evolutionary games in which individuals choose whether to cooperate or defect. We find that increasing the group size decreases the proportion of cooperators at both stable and unstable rest points of the replicator dynamics. This implies that larger group sizes can have negative effects (by reducing the amount of cooperation at stable polymorphisms) and positive effects (by enlarging the basin of attraction of more cooperative outcomes) on the evolution of cooperation. These two effects can be simultaneously present in games whose evolutionary dynamics features both stable and unstable rest points, such as public goods games with participation thresholds. Our theory recovers and generalizes previous results and is applicable to a broad variety of social interactions that have been studied in the literature.
evolution of cooperation; evolutionary game theory; replicator dynamics; public goods games;
- C73: Stochastic and Dynamic Games • Evolutionary Games • Repeated Games
- H41: Public Goods
IAST working paper, n. 18-75, May 2018