Seemingly Unrelated Repeated Games

Suppose Player A is playing two apparently independent repeated games with two other people, B and C, with A randomly matched, each period, with either B or C. Each dyad maintains the maximum incentive-compatible level of cooperation within the dyad, even if cooperation has broken down in the other dyad. Thus, if A defects against B, say, then C is still willing to cooperate with A to the maximum incentive-compatible degree. Nevertheless, we show that the simple presence of each cooperative relationship can increase the maximum incentive compatible level of cooperation in the other dyad, due to a counterintuitive circular reasoning or “bootstrapping” effect. With more than two relationships, bootstrapping effects alternate with equally counterintuitive reverse bootstrapping effects.