The Coase Theorem says that, in an economic transaction with externalities, if property rights are well defined and if the transaction costs are low enough, then the private solution is socially optimal, with no need for government intervention to correct the situation externality, which is a market failure. The government's only role would be to ensure that property rights are well defined and that free trade flows without transaction costs.
Coase's theorem, shows how the role of institutions, especially legal ones, are important for the proper functioning of the market economy.