Ability to separate situations with a priori coalition structures by means of symmetric solutions
Document typeConference lecture
Rights accessRestricted access - publisher's policy
We say that two situations described by cooperative games are inseparable by a family of solutions, when they obtain the same allocation by all solution concept of this family. The situation of separability by a family of linear solutions reduces to separability from the null game. This is the case of the family of solutions based on marginal contributions weighted by coef¿cients only dependent of the coalition size: the semivalues. It is known that for games with four or more players, the spaces of inseparable games from the null game contain games different to zero-game. We will prove that for ¿ve or more players, when a priori coalition blocks are introduced in the situation described by the game, the dimension of the vector spaces of inseparable games from the null game decreases in an important manner.
CitationGimenez, J. Ability to separate situations with a priori coalition structures by means of symmetric solutions. A: International Conference on Operations Research and Enterprise Systems. "ICORES 2017: proceedings of the 6th International Conference on Operations Research and Enterprise Systems: Porto, Portugal, February 23-25, 2017". Porto: 2017, p. 242-249.