Axiomatization and Core Stability of Allocation Rules for Hypergraph Situations

In this paper, we explore network situations where the architecture of the network is described by a hypergraph. In a hypergraph, nodes are the players and - in contrast to bilateral graphs - links between players may involve more than just two players. The value function is defined on the architecture of the network such that different hypergraphs that connect the same individuals can generate different values. We provide axiomatic characterizations for the Myerson value and the position value. Furthermore, we define the notion of the core of a hypergraph situation. By means of an example, we also show that the Myerson value and the position value can lie in the core of a hypergraph situation.