# The Coase Theorem with more than two parties

Let us now return to a world without transaction costs. A natural question is whether the Coase Theorem holds when there are three or more parties. Suppose, for example that there are two factories and a group of residents. The residents must now bargain with both factories if they would like to see a reduction in pollution. Does either version of the Coase Theorem hold in this case?

Even if parties have quasi-linear preferences, the situation now becomes more complicated, relative to our previous example. The reason is that in splitting up the potential surplus that could be realised when the efficient levels of production are chosen, the parties must not only agree on an outcome in which each party receives at least as much as it would if the parties acted alone. The agreement must also be *stable* (in some yet to be defined sense) against possible threats in which two of the parties might reach a superior agreement that gives each of them more than they would receive if the agreement included an additional party. In other words, instead of having just a *single* threat point, each party now has *multiple* threat points, which each can use to their advantage to obtain a better deal. The question we now turn to is whether stable Coasean-type agreements are possible in such a situation, and whether they are invariant to the initial legal rule or allocation of property rights.