However, if the interested parties cannot reach or enforce a bargain, or if the bargaining process incurs a transaction cost, then the externality will not be resolved and will require the intervention of another party, the government.
What Coase originally proposed in 1959 in the context of the regulation of radio frequencies was that as long as property rights in these frequencies were well defined, it did ultimately not matter if adjacent stations would initially interfere with each other by broadcasting in the same frequency band. The station being able to reap the higher economic gain of the two from broadcasting would in this case have an incentive to pay the other station not to interfere. In the absence of transaction costs both stations would strike a mutually advantageous deal. Put differently, it would not matter whether one or the other station had the initial right to broadcast: Eventually, the right to broadcast would end up with the party that was able to put it to the most profitable use.
Coases main point, clarified in an article published in 1960 and cited when he was awarded the Nobel Prize in 1991, was however that transaction costs could not be neglected, and that therefore, the initial allocation of property rights mattered in the presence of side effects (externality).
George Stigler summarised the resolution of the externality problem in the absence of transaction costs in a 1966 economics textbook in terms of private and social cost, and for the first time called a 'theorem' (although no definite mathematical version of it has ever been stated or proved). Nevertheless, since the 1960s, a voluminous literature on the Coase theorem and its various interpretations, proofs, and refutations, has developed that continues to grow.