The in-group egalitarian Owen values

Abstract

This paper proposes a new class of allocation rules, which is referred to as the in-group egalitarian Owen values, that integrates two seemingly conflicting principles—marginalism and egalitarianism—in the framework of cooperative games with coalition structures. This class of allocation rules facilitates the use of different principles of allocation in different layers of a social structure such as allocation across coalitions and within a coalition. Therefore, each coalition can employ its specific distributive principle for intra-coalition distribution. Our main results provide axiomatic foundations for the class of allocation rules, in which monotonicity properties highlight the importance of the proposed solutions. We also show that various monotonicity properties generate various allocation rules, where the Owen value and the in-group egalitarian division value are special cases. These results extend the egalitarian Shapley values to the games with coalition structures and offer a rationale for monotonic allocation rules in the presence of social structures.