Aivazian and Callen (J Law Econ 24(1):175–181, 1981) and a number of their subsequent papers use cooperative game theory and core theory to show that the Coasean efficiency result is not robust when there are more than two players. Drawing primarily on their results, this chapter systematically explains the main argument and its extensions as follows. First, the Coase theorem could break down when there are more than two participants because the core of the negotiations may be empty under one set of property rights and nonempty under another. Second, transaction costs will tend to aggravate the empty core problem and make it more likely that the Coasean efficiency result will fail. Third, Pareto optimality can be achieved when the core is empty by the imposition of constraints on the bargaining process and the use of penalty clauses and binding contracts. Overall, the results indicate that it is important to distinguish between transaction costs (when the core exists) and costs due to the empty core because each has different implications for rationalizing institutions. This chapter also summarizes experimental results indicating that the existence of the core is an important determinant of negotiations generally and the Coase theorem in particular. It also points out that some of the problems raised for Coasean efficiency by the empty core also arise under alternative (non-core) notions of coalitional stability.