Weighted Component Fairness for Forest Games∗

We present the axiom of weighted component fairness for the class of forest games, a generalization of component fairness introduced by Herings, Talman and van der Laan (2008) in order to characterize the average tree solution. Given a system of weights, component efficiency and weighted component fairness yield a unique allocation rule. We pro-vide an analysis of the set of allocation rules generated by component efficiency and weighted component fairness. This allows us to provide a new characterization of the random tree solutions. Key words: (Weighted) component fairness – Core – Graph games – Alexia value – Harsanyi solutions – Random tree solutions.