Parameterized fairness axioms on cycle-free graph games

  • Authors:

  • S. Ryuo;K. Sato;Y. Yamamoto

  • Affiliations:

  • Transport Information Technology Division, Railway Technical Research Institute, Kokubunji-shi, Japan 185-8540;Transport Information Technology Division, Railway Technical Research Institute, Kokubunji-shi, Japan 185-8540;Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki, Japan 305---8573

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2012

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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.