The Myerson Value and Superfluous Supports in Union Stable Systems

Abstract

Cooperative games with partial cooperation cover a wider rank of real world situations than the classic model of cooperative games where every subset of a set of agents can form a coalition to execute the game. In this paper, the set of feasible coalitions which models the partial cooperation will be given by a union stable system. These systems contain, as particular cases, the communication situations and the permission structures, which are well-known both from a theoretical and applied point of view. Moreover, union stable systems are a natural framework for many other economic situations that arise in practice and which can not be modelled by these subsystems. In this paper, the goal is to make clear that there exists a close relationship between the Myerson value and the so-called conference game which player set consists of the supports of the union stable system. For that, we first analyze the relation between the restricted game and the conference game to establish later which effects a union stable system has on certain desirable properties of these games. Using the superfluous support property, defined through the conference game, new characterizations for the Myerson value are given in this context.