Peer discipline and incentives within groups

• We study how a group can sustain non-Nash actions through peer discipline.
• Punishment is recursive: failure to punish may be punished.
• Optimal plans are characterized.
• The model is applied to a public good contribution problem.
• Large groups achieve members’ contribution iff peer discipline is available.

We investigate how a collusive group can sustain non-Nash actions by enforcing internal discipline through costly peer punishment. We give a simple and tractable characterization of schemes that minimize discipline costs while preserving incentive compatibility. We apply the model to a public goods contribution problem. We find that if the per-capita benefit from the public good is low, then regardless of whether peer discipline is feasible or not only small groups will contribute to the good. If the public good benefit is significant but peer discipline is infeasible it remains the case that only small groups contribute. On the other hand, if the public good benefit is significant but peer discipline is feasible then full contribution takes place regardless of group size. We reconcile this result with Olson's idea that small groups are more effective by considering the case where the per-capita benefit of the public good varies with group size.