Splitting graphs when calculating Myerson value for pure overhead games

Abstract

A communication situation consists of a coalitional game and a graph, the nodes of the graph corresponding to the players of the game. To calculate the Myerson value for such situations, we obtain results which extend those well known for trees and cycle-complete graphs. On the other hand, in order to reduce the associated calculus for communication situations with a pure overhead game, the possibility of splitting the graph in several subgraphs is analyzed. For each fixed decomposition of the graph, a subspace of games compatible with this decomposition is given.