On the core of Aubin extension of almost positive game

The aim of the paper is to study the core of the famous Aubin extension for almost positive games. These games are characterized by nonnegativity of the Harsanyi dividends of their non-singleton coalitions. So, being convex, these games have their Shapley values inside the classical core. We prove that for the Aubin extension of these games much more stronger result holds: the core of this extension of any almost positive game consists of its Shapley value only. The approach developed is based, mostly, on close relation between the cores and super-differentials of fuzzy cooperative games, mentioned by J. -P. Aubin.