We present a noncooperative bargaining protocol among n players, applied to the setting of cooperative games in coalitional form with transferable utility. In this model, players are chosen randomly to make proposals until one is accepted unanimously, and after each proposal rejection, the...

A new axiomatic characterization of the two-step Shapley value (Kamijo, 2009) is presented based on a solidarity principle of the members of any union: when the game changes due to the addition or deletion of players outside the union, all members of the union will share the same gains/losses.

The family of discounted Shapley values is analyzed for cooperative games in coalitional form. We consider the bargaining protocol of the alternating random proposer introduced in Hart and Mas-Colell (1996). We demostrate that the discounted Shapley values arise as the expected payoffs...

A value for games with a coalition structure is introduced, where the rules guiding the cooperation among the members of the same coalition are different from the interaction rules among coalitions. In particular, players inside a coalition exhibit a greater degree of solidarity than they are...