What is the relationship or difference between Nash and Coasian bargaining solutions? It is well-known that the Nash bargaining solution satisfies certain basic axioms. Which of these does the Coasian solution satisfy? Is the Nash solution applicable when there are externalities, and are the two solutions same/comparable in any sense?
There is no such thing as the "Coasian bargaining solution". This is a simple principle according to which parties find an agreement somewhere on the Pareto frontier when they bargain, which means that the outcome of the bargaining process is socially efficient (abstracting from equity issues).
The Nash bargaining solution refines our predictions by specifying where the solution is likely to be located on the Pareto frontier. In some sense, it is a subset of the Coasian bargaining outcome, which can be anywhere on the Pareto frontier. In contrast to the Coase principle, it is a theorem that rests on an axiomatic characterization.