Cooperative Games and Coalition Cohesion Indices: The Choquet–Owen Value

Abstract

In a cooperative game with transferable utility, it is usually assumed that all coalitions are equally feasible. However, if we deal with cooperative games with coalition configuration, only some coalitions are a priori feasible, due to the preferences of the agents. In this paper, we propose a generalization of games with coalition configuration. In our model, the feasibility of a coalition is determined by the cohesion of its members, and obviously, this cohesion does not have to be equal for all coalitions. The cohesion of each coalition will be determined by a cohesion index. We introduce the class of games with cohesion index and propose an allocation rule, which is characterized by using reasonable properties. The cohesion idea is not only a concept related to social groups. In software design, this concept explains the relationships among all the elements of a module. Our value can be applied in this way as we show in the paper.