The Shapley value analyzed under the Felsenthal and Machover bargaining model

In 1996, Felsenthal and Machover proposed a bargaining procedure for a valuable payoff in cooperative and simple games. They proved that the value underlying their bargaining scheme was the Shapley value by showing that it verifies the axioms that Shapley proposed for characterizing his value. They remarked that a direct proof of the result involves rather formidable combinatorial difficulties, but that it has some independent interest. In this paper, we prove such a combinatorial result and obtain a formula for the Shapley value that has a great potential to be extended to more general classes of games.