Parameterized fairness axioms on cycle‐free graph games

We study cooperative transferable utility games with a communication structure represented by an undirected graph, i.e., a group of players can cooperate only if they are connected on the graph. This type of games is called graph games and the best‐known solution for them is the Myerson value, which is characterized by the component efficiency axiom and the fairness axiom. Recently the average tree solution has been proposed on cycle‐free graph games, and shown to be characterized by the component efficiency axiom and the component fairness axiom. We propose ϵ‐parameterized fairness axiom on cycle‐free graph games that incorporates the preceding fairness axioms, and show the existence and the uniqueness of the solution. We then discuss a relationship between the existing and our proposed solutions by a numerical example.