On the Size and Structure of Group Cooperation

This paper examines characteristics of cooperative behavior in a repeated, n-person, continuous action generalization of a Prisoner's Dilemma game. When time preferences are heterogeneous and bounded away from one, how does group cooperation vary with the group's size and structure? For an arbitrary distribution of discount factors, we characterize the maximal average cooperation (MAC) likelihood of this game. The MAC likelihood is the highest average level of cooperation, over all stationary subgame perfect equilibrium paths, in the group. We show that the MAC likelihood is increasing in monotone shifts, and decreasing in mean preserving spreads, of the distribution of discount factors. This suggests that more heterogeneous groups are less cooperative. Finally, we show under certain conditions that the MAC likelihood exhibits increasing returns to scale when discounting is heterogeneous: larger groups are more cooperative than smaller ones. By contrast, when discounting is homogeneous, the MAC likelihood is invariant to group size.