Nash bargaining solution with coalitions and the joint bargaining paradox

We propose a solution for bargaining problems where coalitions are bargainers. The solution generalizes the Nash solution and allows one to interpret a coalition as an institutional player whose preferences are obtained by aggregating the preferences of the individual members. One implication of our solution is that forming a coalition is unprofitable in pure-bargaining situations (the joint-bargaining paradox). We show, however, that forming a coalition can be profitable in a non-pure bargaining situation.