Resilient Cooperators Stabilize Long-Run Cooperation in the Finitely Repeated Prisoner's Dilemma

The dynamics of learning in finitely repeated games of cooperation remains an open question in large part because the timescale on which learning takes place is much longer than that of traditional lab experiments. Here we report results of a “virtual lab” experiment in which 94 subjects play up to 400 ten-round games of Prisoners Dilemma over the course of twenty consecutive weekdays. Consistent with previous work, the typical round at which players first defect creeps steadily earlier over the first several days; however, this unraveling process slows after roughly one week and remains stable for the rest of the experiment. Analyzing individual strategies shows that roughly 40% of players resist the temptation to unravel, cooperating conditionally throughout the experiment, even at a significant cost to themselves. We call these players resilient cooperators. Finally, using a standard learning model we predict that the presence of more than a critical fraction of resilient cooperators can permanently stabilize unraveling among a majority of rational players. These results shed new and hopeful light on the long-term dynamics of cooperation, and demonstrate the importance of conducting behavioral experiments on longer timescales than previously contemplated.