Group size and cooperation among strangers

• We model an n-person PD game with anonymous and randomly matched agents.
• We show that it can be easier to sustain society-wide cooperation with a larger group size.
• Strong experimental evidence is provided for this theoretical prediction when there is no strategic uncertainty.
• The introduction of strategic uncertainty may diminish this group size effect.

We study how group size affects cooperation in an infinitely repeated n-player Prisoner's Dilemma (PD) game. In each repetition of the game, groups of size n ≤ M are randomly and anonymously matched from a fixed population of size M to play the n-player PD stage game. We provide conditions for which the contagious strategy ( Kandori, 1992) sustains a social norm of cooperation among all M players. Our main finding is that if agents are sufficiently patient, a social norm of society-wide cooperation becomes easier to sustain under the contagious strategy as n increases toward M. In an experiment where the population size M is fixed and conditions identified by our theoretical analysis hold, we find strong evidence that cooperation rates are higher with larger group sizes than with smaller group sizes in treatments where each subject interacts with M − 1 robot players who follow the contagious strategy. When the number of human subjects increases in the population, the cooperation rates decrease significantly, indicating that it is the strategic uncertainty among the human subjects that hinders cooperation.