Chapter summary

In this chapter we present the bargaining set, which is a set solution concept for coalitional games. The idea behind the bargaining set is that when the players consider how to divide the worth of a coalition among themselves, a player who is unsatisfied with the suggested imputation can object to it. An objection, which is directed against another player, roughly claims: “I deserve more than my suggested share and you should transfer part of your suggested share to me because …” The player against whom the objection is made may or may not have a counterobjection. An objection that meets with no counterobjection is a justified objection. The bargaining set consists of all imputations in which no player has a justified objection against any other player.

It follows from the definition of an objection that in any imputation in the core no player has an objection, and therefore the core is always a subset of the bargaining set. It is proved that contrary to the core, the bargaining set is never empty. In convex games the bargaining set coincides with the core.