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 eciency and weighted component fairness yield a unique allocation rule. We provide an analysis of the set of allocation rules generated by component eciency and weighted component fairness. This allows us to provide a new characterization of the random tree solutions.