Nash-in-Shapley : Bilateral Bargaining with Recursive Threat Points

We examine the role of competition and mergers in bargaining by embedding a performance game, in which retail prices are determined by competition, into an axiomatic bilateral bargaining model, in which suppliers and retailers negotiate wholesale terms. We prove existence and uniqueness of what we call the Nash-in-Shapley bargaining solution when threat points are built up recursively, from the set of agreements that would result absent each agreement. We compare and contrast outcomes to those in Nash-in-Nash and conclude Nash-in-Shapley is a useful addition to the competition toolbox, though when to use it depends, as always, on how well it captures significant features of competition