A value for bi-cooperative games

Abstract : Bi-cooperative games were introduced by Bilbao et al. as a generalization of TU cooperative games, in which each player can participate positively, negatively, or not at all. In this paper, we propose a definition of a share of the worth obtained by some players after they decided on their participation in the game. It turns out that the cost allocation rule does not look for a given player to her contribution at the opposite participation option to the one she chooses. The relevance of the value is discussed on several examples.
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Christophe Labreuche, Michel Grabisch. A value for bi-cooperative games. International Journal of Game Theory, Springer Verlag, 2008, 37 (3), pp.409-438. ⟨10.1007/s00182-008-0126-5⟩. ⟨halshs-00308738⟩

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