Set-valued Tu-games 3

8 Abstract 9 The goal of this paper is to explore solution concepts for set-valued TU-games. Several stability conditions can be 10 defined since one can have various interpretations of an improvement within the multicriteria framework. We present 11 two different core solution concepts and explore the relationships among them. These concepts generalize the classic 12 core solution for scalar games and can be considered under different preference structures. We give characterizations for 13 the non-emptiness of these core sets and apply the results to four multiobjective operational research games. 17 It is currently accepted that real-world decision processes are multivalued. This assertion means that 18 decision-making is actually based on several (more than one) criteria. Obviously, using several criteria 19 implies the non-existence of a total order among the evaluation of the different alternatives. Thus, regarding 20 the scalar case, where all the optimal decisions share the same evaluation, in multicriteria decision-making 21 the above property does not make sense. In the latter case, the decision-maker may accept many different 22 alternatives provided that their evaluations are non-dominated componentwise. 23 Modelling conflict situations where several criteria must be considered simultaneously leads in a natural 24 way to multiobjective game theory (see e. In this framework the evaluation given to the alternatives considered by the agents is 26 not a unique value but a set of non-dominated vectors (see Fern a andez et al. 28 The discussion above leads us to consider the class of the multiobjective cooperative TU-games. Within 29 this class any coalition S of player is given a characteristic set of vectors. These vectors represent the non