Allocation Rules for Hypergraph Games

Abstract

We extend the approach of van den Nouweland et al. (1992) towards hypergraph games and provide axiomatic characterizations for the Myerson value and the position value. We assume that players are connected in a conference structure that is described by a hypergraph and in which players in a conference can communicate and negotiate plans. In contrast to a cooperative game, the value function is defined on the conference structure, as in network games, since we allow different hypergraph structures that connect the same individuals to lead to different values. Furthermore, we define the notion of the core of a hypergraph game and show by means of an example that the Myerson value and the position value can lie in the core of a hypergraph game.