Abstract: We study the additive decomposition of the Position value on hypergraph games. In 1988, Meessen considered the contributions of the links in the alliances and proposed an important allocation rule, called the Position value. By considering each conference in hypergraphs not only affects the benefit of the players in the alliances associated with it, but also affects the benefit of the players in the alliances that are not associated with it, we introduce the within groups Position value and the between groups Position value on hypergraph games to distinguish the components of each player’s benefit. We first give axiomatic characterizations for these two kinds of values. Secondly, we give an example to illustrate the within groups Position value and the between groups Position value. Finally, we propose an improved allocation rule by adjusting the proportion of the intermediary cost.

Key words: TU game, hypergraph, hypergraph game, Position value