In markets with avoidable fixed costs, the core may be empty. The author argues that a reason for collusion is to impose an equilibrium where none exists. He sets up a framework for deriving testable implications from the model and compares those implications with those of a cartel model. The author compares the two models empirically with data from liner shipping conferences, legal collusive agreements that have been in force for over a century, and concludes that the evidence supports the theory of the core.