Transaction costs can encourage Coasean bargaining

When there are three parties, instability problems brought about by the emptiness of the core of the corresponding cooperative game may cause the Coase Theorem to fail, even when other more direct impediments to bargaining are low. We show that the standard Coasean bargaining game involving three parties is strategically equivalent to an asymmetric three-player majority game. Hence, when there are three parties, instability problems will cause the Coase Theorem to fail if and only if the core of the corresponding three-player majority game is empty. We use this equivalence result to derive all instances in which the Coase Theorem will and will not hold with three parties, and show that a priori, such instability problems are likely to be rare—the Coase Theorem will actually hold most (over 80 %) of the time. We also demonstrate that it is always possible to find a set of transaction costs which, when introduced into a frictionless bargaining situation, will cause an empty core to become non-empty. In other words, transaction costs can mitigate instability problems: situations exist in which the presence of transaction costs will cause the Coase Theorem to hold when, in the absence of those direct transaction costs, it would fail to hold. When there are three parties, rather than hindering agreements, the existence of direct transaction costs can sometimes—but not always—reduce instability and encourage Coasean bargaining.