Efficient extensions of communication values

We study values for transferable utility games enriched by a communication graph. The most well-known such values are component-efficient and characterized by some link-deletion property. We study efficient extensions of such values: for a given component-efficient value, we look for a value that (i) satisfies efficiency, (ii) satisfies the link-deletion property underlying the original component-efficient value, and (iii) coincides with the original component-efficient value whenever the underlying graph is connected. Béal, Casajus and Huettner (forthcoming, Scoail Choice and Welfare) prove that the Myerson value (Myerson, 1977) admits a unique efficient extension, which has been introduced by van den Brink, van der Laan and Khmelnitskaya (2012). We pursue this line of research by showing that the average tree solution (Herings, van der Laan and Talman, 2008) and the compensation solution (Béal, Rémila and Solal, 2012) admit similar unique efficient extensions, and that there exists no efficient extension of the position Value (Meessen, 1988, Borm, Owen and Tijs, 1992). As byproducts, we obtain new characterizations of the average tree solution and the compensation solution, and of their efficient extensions.