Harsanyi extensions and the cores of almost positive games

In the paper, we introduce and study so-called Harsanyi extensions of the finite TU cooperative games. By applying sub-differential calculus we obtain complete description of the cores for the Harasanyi extensions of the almost positive games. For each such a game, realizability of any standard core-imputation as the unique un-blockable payoff of an appropriate Harsanyi extension of the game under consideration is established.