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A Value for Graph-Restricted Games with Middlemen on Edges

Author

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  • Antonio C. Alarcón

    (Departamento de Ciencias Integradas, Facultad de Ciencias Experimentales, Universidad de Huelva, 21007 Huelva, Spain
    These authors contributed equally to this work.)

  • José M. Gallardo

    (Departamento de Matemática Aplicada II, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, 41092 Sevilla, Spain
    These authors contributed equally to this work.)

  • Andrés Jiménez-Losada

    (Departamento de Matemática Aplicada II, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, 41092 Sevilla, Spain
    These authors contributed equally to this work.)

Abstract

In a cooperative game with a communication structure, a graph describes the communication possibilities of the players, which are represented by the nodes. We introduce a variation of this model by assuming that each edge in the communication graph represents an agent. These agents simply act as intermediaries, but since they are essential for the cooperation and, consequently, for revenue generation, they will claim their share of the profit. We study this new model of games with a communication structure and introduce an allocation rule for these games. The motivation for analyzing this type of problem is based on the construction of a risk index for the different elements of an internal network.

Suggested Citation

  • Antonio C. Alarcón & José M. Gallardo & Andrés Jiménez-Losada, 2022. "A Value for Graph-Restricted Games with Middlemen on Edges," Mathematics, MDPI, vol. 10(11), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1856-:d:826609
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    References listed on IDEAS

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    1. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    2. Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Other publications TiSEM 5a8473e4-1df7-42df-ad53-f, Tilburg University, School of Economics and Management.
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