  The Mayser value (Myerson (1977)), the position value (Meessen (1988)) and
the average tree solution (Herings et al.) are three most important allocation
rules for (graph or hypergraph) communication situations. In 2005, an axiomatic
characterization of the position value for arbitrary (graph) communication
situations was given by Slikker (2005). However, an axiomatic characterization
of the position value for arbitrary hypergraph communication situations has not
yet been found and remains an open problem. In our manuscript, we first give
two non-axiomatic characterizations of the position value for hypergraph
communication situations by introducing the uniform hyperlink game and the
$k$-augment uniform hyperlink game. Based on the non-axiomatic
characterizations, we provide an axiomatic characterization of the position
value for arbitrary hypergraph communication situations by employing component
efficiency and partial balanced conference contributions.
