Abstract: In graph games or hypergraph games, Myerson assumed that feasible coalitions are required to be connected, but their structures may be quite different. In 1996, the Myerson value was extended by Jackson and Wolinsky and they generalized the Myerson's model to the "network situations"，or simply "network game". The characteristic function is replaced by the value function to reflect the influence of the structure on the benefits of cooperative coalitions. In other words, the coalitions of different structures may produce different utility. In this paper we consider the hypernetwork situations, or simply "hypernetwork game", which is a natural extension of the network game. It consists of a triple (N,H,v) where (N,H) is a hypernetwork and v is the value function to describe the possible gains from cooperation and in which a network (N, H)describes the restricted cooperation possibilities between the players. In 2012, van den Nouweland and slikker characterized the position value axiomatically for the network game by using four axioms. By introducing a new axiom called partial balanced conference contributions, and combining the component efficiency and the additive property, we propose an axiomatic characterization of the position value for the hypernetwork situations. Finally, one example illustrate the characteristic theorem.

Key words: Hypernetwork situation, position value, component efficiency, partial balanced conference contributions