The core of bicapacities and bipolar games

Bicooperative games generalize classical cooperative games in the sense that a player is allowed to play in favor or against some aim, besides nonparticipation. Bicapacities are monotonic bicooperative games, they are useful in decision making where underlying scales are of bipolar nature, i.e., they distinguish between good/satisfactory values and bad/unsatisfactory ones. We propose here a more general framework to represent such situations, called bipolar game. We study the problem of finding the core of such games, i.e., the set of additive dominating games.