Abstract
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 \({\epsilon}\) -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.
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Ryuo, S., Sato, K. & Yamamoto, Y. Parameterized fairness axioms on cycle-free graph games. J Glob Optim 52, 487–497 (2012). https://doi.org/10.1007/s10898-011-9761-7
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DOI: https://doi.org/10.1007/s10898-011-9761-7