Characterizations of the position value for hypergraph communication situations

Abstract

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.