Bargaining with commitments

We study a simple bargaining mechanism in which, given an order of players, the first n–1 players sequentially announce their reservation price. Once these prices are given, the last player may choose a coalition to cooperate with, and pay each member of this coalition his reservation price. The only expected final equilibrium payoff is a new solution concept, the selective value, which can be defined by means of marginal contributions vectors of a reduced game. The selective value coincides with the Shapley value for convex games. Moreover, for 3-player games the vectors of marginal contributions determine the core when it is nonempty.A previous version of this paper has benefited from helpful comments from Gustavo Bergantiños. Numerous suggestions of two anonymous referees, the Associate Editor, and William Thomson, Editor, have led to significant improvements of the final version. Financial support by the Spanish Ministerio de Ciencia y Tecnología and FEDER through grant BEC2002-04102-C02-01 and Xunta de Galicia through grant PGIDIT03PXIC30002PN is gratefully acknowledged.