Multiobjective n-person cooperative games

Abstract

In this chapter, we investigate multiobjective n-person cooperative games. First of all, as a topic related to the multiobjective games, we consider n- person cooperative games under fuzziness, uncertainty or risk. To introduce fuzziness, uncertainty or risk into a cooperative game, we define a mapping which associates a coalition with a fuzzy set or a probability distribution, instead of the characteristic function. A representation of cooperative games in which a coalition value is represented as a random variable has already been studied by Charnes and Granot [29, 30] . The cooperative game under uncertainty is formally represented as a cooperative game with vector-valued characteristic function. Such games were also investigated by Bergstresser and Yu [11] in the study on multiobjective games. They called such games multiobjective cooperative games but we think it would be appropriate to call them cooperative games with multiple scenarios or cooperative games under uncertainty. Bergstresser and Yu mainly considered the core defined by the domination structures and referred to a couple of solution concepts which yield a unique solution such as the nucleolus in n-person cooperative games. Sakawa and Nishizaki considered the nucleolus in n-person cooperative games with multiple scenarios [121].