Weighted values and the core in NTU games

The purpose of this paper is to extend the following result by Monderer et al. (1992): the set of weighted Shapley values includes the Core in TU games. We extend the result to the class of uniformly positively smooth NTU games. We focus on two solution concepts which extend the weighted Shapley value. First, we focus on the weighted Egalitarian solution introduced by Kalai and Samet (1985). We show that the set of weighted Egalitarian solutions includes the Core. Second, we focus on a new solution concept which we call the consistent weighted Shapley value. The solution concept is defined by extending the consistent Shapley value by Maschler and Owen (1989). We show that, if the attainable payoff for grand coalition is represented by a closed half-space of a hyperplane, then the set of consistent weighted Shapley values includes the Core. JEL classification: C71