Harsanyi Extensions and the Cores of Almost Positive Games

In the paper, we introduce and study the so-called Harsanyi extensions of finite TU cooperative games. A complete description of the cores for the Harsanyi extensions of almost positive games is obtained by applying sub-differential calculus. For each such a game, we establish that any standard core imputation is represented as a unique unblockable payoff of an appropriate Harsanyi extension of the game under consideration.