Centrality Rewarding Shapley and Myerson Values for Undirected Graph Games

In this paper we introduce two values for cooperative games with communication
graph structure. For cooperative games the shapley value distributes the worth of
the grand coalition amongst the players by taking into account the worths that can
be obtained by any coalition of players, but does not take into account the role of
the players when communication between players is restricted. Existing values for
communication graph games as the Myerson value and the average tree solution
only consider the worths of connected coalitions and respect only in this way the
communication restrictions. The two values take into account the position of a
player in the graph. The rst one respects centrality, but not the communication
abilities of any player. The second value reflects both centrality and the commu-
nication ability of each player. That implies that in unanimity games players that
do not generate worth but are needed to connect worth generating players are
treated as those latter players, and simultaneously players that are more central
in the graph get bigger shares in the worth than players that are less central. For
both values an axiomatic characterization is given on the class of connected cycle-free graph games.