Notes on a new compromise value: The <inf>x</inf>-value

We introduce and study a new compromise value for all weakly essential transferable utility games: the x-value. It is closely related to the τ-value defined by Tijs in 1981. The main difference being the way we define the maximal aspiration a player may have in the game: instead of considering the marginal contribution to the grand coalition, we consider his maximal (among all coalitions) marginal contribution. We show that the class of games where the new value can be applied is larger.