On the Core of the Aubin Extension of an Almost PositiveGame

We analyze connections between the Shapley value and the core of the well-known Aubin extension of an almost positive cooperative game. Nonnegative Harsanyi dividends characterize such games up to an additive component. Since each almost positive game is convex, its core contain the Shapley value. We prove a stronger connection for the Aubin extension of such a game; namely, the core is a singleton consisting of the corresponding Shapley value. Aubin mentioned that, for certain classes of fuzzy cooperative games, it is possible to describe the core in terms of the superdifferential of the characteristic function. Our arguments are based on this fact.