Bargaining property of nucleolus and tau-value in a class of TU-games

First, we introduce pairwise-bargained consistency with a reference point, and use as reference points the maxmin and the minmax value within pure str ategies of a certain constant-sum bimatrix game, and also the game Value wi thin mixed strategies of it. Second, we show that the pairwise-bargained co nsistency with reference point being the maxmin or the minmax value determi nes the nucleolus in some class of transferable utility games. (This result is known in the bankruptcy games and the pseudoconcave games with respect to supersets of the managers.) This class of games whose element we call a pseudoconcave game with respect to essential coalitions, of course, include s the bankruptcy games and the pseudoconcave games with respect to superset s of the managers. It is proved that this class of games is exactly the sam e as the class of games which have a nonempty core that is determined only by one-person and (n - 1)-person coalition constraints. And we give a suffi cient condition which guarantees that the bargaining set coincides with the core in this class of games. Third, we interpret the tau -value of a quasi balanced transferable utility game by the pairwise-bargained consistency wi th reference point being the game Value. Finally by combining the second an d the third results, if a transferable utility game in this class is also s emiconvex, then the nucleolus and the tau -value are characterized by the p airwise-bargained consistency with different reference points which are giv en by the associated bimatrix game. (C) 2001 Elsevier Science Ltd. All righ ts reserved.