A value for bi-cooperative games

Christophe Labreuche (1) , Michel Grabisch (2)

1 Laboratoire Albert Fert (ex-UMPhy Unité mixte de physique CNRS/Thales)
2 CES - Centre d'économie de la Sorbonne

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.

Mots clés: Bi-cooperative games; Value; Efficiency

Domaines: Economies et finances; Recherche opérationnelle [math.OC]; Informatique et théorie des jeux [cs.GT]

Christophe Labreuche, Michel Grabisch. A value for bi-cooperative games. International Journal of Game Theory, 2008, 37 (3), pp.409-438. ⟨10.1007/s00182-008-0126-5⟩. ⟨halshs-00308738⟩