Coase had brilliant insight into economics and the market. Simply if there existed enforceable property rights in everything, and the transaction costs were de minimis, then the market could clear any inefficiencies in distribution.
A recent example was discussed by Marron which I believe is close but not quite there, namely I believe it is not Coasian. The case is water rights, the upstream users and the downstream.
Take the Hudson River. Those up stream, say in Albany, dump junk in the river and those down stream, say the west Bronx, end up with trash. Thus Marron articulates two solutions:
First, the Government intervenes and establishes all sorts of rules, all with unintended consequences.
Second, and this is where I believe he is off, those in the Bronx pay those in Albany not to do what they have been doing. To anyone who knows New York that is what is happening already. The Legislators are dumping trash in the River and then they also tax those down stream, but the trash never stops!
The Coasian solution I believe is the following. The water use is a defined property right. The Government's sole role is to enforce the right. The down river people notice the junk and they sue those up river who pollute. The Government enforces the property right and the up river folk pay compensation to down river folk. They also clean up the river.
Coase did not think bribes were the solution. Property rights were and the Government's role in enforcing them.