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New allocation rule of directed hypergraphs

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  • Taiki Yamada

Abstract

The Shapley value, one of the well-known allocation rules in game theory, does not take into account information about the structure of the graph, so by using the Shapley value for each hyperedge, we introduce a new allocation rule by considering their first-order combination. We proved that some of the properties that hold for Shapley and Myerson values also hold for our allocation rule. In addition, we found the relationship between our allocation rule and the Forman curvature, which plays an important role in discrete geometry.

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  • Taiki Yamada, 2021. "New allocation rule of directed hypergraphs," Papers 2110.06506, arXiv.org, revised Feb 2023.
    • Handle: RePEc:arx:papers:2110.06506
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    References listed on IDEAS

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    1. Sylvain Béal & André Casajus & Frank Huettner, 2015. "Efficient extensions of the Myerson value," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 819-827, December.
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    4. Neyman, Abraham, 1989. "Uniqueness of the Shapley value," Games and Economic Behavior, Elsevier, vol. 1(1), pages 116-118, March.
    5. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
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    7. E. Algaba & J. M. Bilbao & P. Borm & J. J. López, 2001. "The Myerson value for union stable structures," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(3), pages 359-371, December.
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