Operations Research seminar

The degree value for games with communication structure

Guang Zhang, Erfang Shang, Guangming Wang

School of Management, Shanghai University, Shanghai 200444, P.R. China

Abstract:

We introduce a new value concept for TU games with hypergraph communication structure, the so-called degree value, by employing the degree game induced by the given game with hypergraph communication structure, in particular, with graph communication structure. The degree value highlights the importance of a player's degree in a communication hypergraph. For arbitrary hypergraph communication structures we provide an axiomatic characterization of the degree value by applying component efficiency and balanced conference contributions, which is a natural extension of balance link contributions introduced in Slikker (Int J Game Theory 33: 505–514, 2005) for games with graph communication structure. We show that in general the degree value differs from both the Myerson value and the position value for games with hypergraph communication structure, but in case of a uniform hypergraph communication structure, in which every conference contains the same number of players, the degree value coincides with the position value.