Multilateral interactions improve cooperation under random fluctuations

In an environment subject to random fluctuations, when does an increase in the breadth of activities in which individuals interact together help foster collaboration on each activity? We show that when players, on average, prefer to stick to a cooperative agreement rather than reneging by taking their privately optimal action, then such an agreement can be approximated as equilibrium play in a sufficiently broad relationship. This is in contrast to existing results showing that a cooperative agreement can be sustained only if players prefer to adhere to it in every state of the world. We consider applications to favor exchange, multimarket contact, and relational contracts.