Read this original piece of literature written by James M. Buchanan, who explains the Coase Theory.
In his basic paper, Coase did not carefully make a distinction between the assignment of rights to particular individuals and the rules determining the liability of particular individuals for damage that their behavior might impose on others. His example, the now-familiar one of the interaction between the rancher and the farmer, was discussed in terms of alternative rules for bearing liability for damages. Either the rancher, whose cattle strayed onto the neighboring croplands, was liable for damages that the farmer might suffer, or he was not liable. If both cattle and grain were marketed competitively, the neutrality theorem showed that the same allocative outcome would be generated, regardless of which set of liability rules should be in existence. In the former case, the rancher, knowing in advance that he would be liable for damages caused by his straying animals, would include these payments as an anticipated cost in making his size-of-herd decisions. In the latter case, the farmer, knowing that he can collect no damages from the rancher (and that he must respect the property rights of the rancher to cattle), will find it advantageous to initiate payments to the latter in exchange for agreements limiting the size of herd, if indeed the value of crop damage at the margin exceeds the value of the additional grazing to the rancher.
Coase overlooked the fact that the institutional structure was significantly different in the two cases. In the second case, the shift toward an efficient outcome takes place through an ordinary market or exchange process, in which none other than the two parties need get involved. In the first case, however, as presented by Coase, there must be third-party interference by a "judge" to assess charges for damage that has been done. In the context of his discussions, this institutional difference does not matter, since the third-party can, presumably, measure and assess damages with complete accuracy. The difference is nonetheless important in the more general setting. Consistency should have dictated that the first case be presented, not as one where the rancher was liable ex post for damages caused by his straying animals, but as one where the farmer held enforceable property rights in his croplands, rights that were inviolate except on his own agreement. In this framework, the rancher would have had to negotiate an agreement with the farmer in advance of any actual straying of cattle. This converts the institutional setting on this side into one that is parallel to the converse case. No third party, no judge, is required to intervene and to assess damages ex post.
We may define this setting as one in which property rules are established and enforced, as opposed to liability rules. This setting calls direct attention to the motivation that both parties have to exploit the potentially realizable surplus by moving from the initial efficient position. This setting also allows for an extension of the neutrality-efficiency theorem beyond those strictly objectifiable circumstances suggested to be present in the Coase example. If the precise degree of damage caused by external imposition is ambiguous, the third party must necessarily exercise his own best judgment in making a settlement. By contrast, if property rules are defined, with the necessity of prior agreement on the part of the potentially damaged party, the latter's own subjective assessment of potential damage becomes controlling in determining the range over which final outcomes may settle. This assessment is, of course, a better measure of actual value lost than the estimate made by any third party.