On the convexity of communication games (Q811421)

A communication situation consists of a game and a communication graph. By introducing two different types of corresponding communication games, point games and arc games, the Myerson value and the position value of a communication situation are introduced. This paper investigates relations between convexity of the underlying game and to the two communication games. In particular, assuming the underlying game to be convex, necessary and sufficient conditions on the communication graph are provided such that the communication games are convex. Moreover, under the same conditions, it is shown that the Myerson value and the position value are in the core of the point game. Some remarks are made on superadditivity and balancedness.