An Axiomatization of the Myerson Value

Authors

  • Özer Selçuk Tilburg University
  • Takamasa Suzuki Tilburg University

Abstract

TU-games with communication structure are cooperative games with transferable utility where the cooperation between players is limited by a communication structure represented by a graph on the set of players. On this class of games, the Myerson value is one of the most well-known solutions and it is the Shapley value of the so-called restricted game. In this study we give another form of fairness axiom on the class of TU-games with communication structure so that the Myerson value is uniquely characterized by this fainess axiom with (component) efficiency, a kind of null player property and additivity. The combination is similar to the original characterization of the Shapley value.

Keywords:

Cooperative TU-games, communication structure, Myerson value, Shapley value

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References

Borm, P., G. Owen, and S. Tijs (1992). On the position value for communication situations. SIAM Journal of Discrete Mathematics, 5, 305–320.

Brink, R. van den (2002). An axiomatization of the Shapley value using a fairness property. International Journal of Game Theory, 30, 309–319.

Brink, R. van den (2009). Comparable axiomatizations of the Myerson value, the restricted Banzhaf value, hierarchical outcomes and the average tree solution for cycle-free graph restricted games. Tinbergen Institute Discussion Paper 2009–108/1, Tinbergen Institute, Amsterdam.

Myerson, R. B. (1977). Graphs and cooperation in games, Mathematics of Operations Research, 2, 225–229.

Shapley, L. (1953). A value for n-person games. In: Kuhn, H.W. and A.W. Tucker (eds.), Contributions to the Theory of Games, Vol. II, Princeton University Press, Princeton, pp. 307–317.

Young, H. P. (1985). Monotonic solutions of cooperative games. International Journal of Game Theory, 14, 65–72.

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Published

2022-08-09

How to Cite

Selçuk, Özer, & Suzuki, T. (2022). An Axiomatization of the Myerson Value. Contributions to Game Theory and Management, 7. Retrieved from https://gametheory.spbu.ru/article/view/13621

Issue

Vol. 7 (2014)

Section

Articles

License

Articles of "Contributions to Game Theory and Management" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.