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A Family of Position Values for Directed Communication Situations

Author

Listed:
  • Elena C. Gavilán

    (Faculty of Statistics, Complutense University of Madrid, Puerta de Hierro, 1, 28040 Madrid, Spain
    These authors contributed equally to this work.)

  • Conrado M. Manuel

    (Faculty of Statistics, Complutense University of Madrid, Puerta de Hierro, 1, 28040 Madrid, Spain
    These authors contributed equally to this work.)

  • René Van Den Brink

    (Department of Economics, Vrije University Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands
    These authors contributed equally to this work.)

Abstract
In this paper, we define a family of values for directed communication situations that are inspired by the position value. We use the concept of directed communication and related connectedness in directed graphs, under which a coalition of players in a game can only cooperate if these players form a directed path in a directed communication graph. By defining an arc game, which assesses the worth of coalitions of (directed) arcs in generating worth, we allocate the Shapley value payoff of each arc over the nodes incident with this arc, where we allow the head and tail to obtain a different share in this arc payoff. However, the way that the arc payoff is shared over its head and tail is uniform over all arcs. We characterize these values by connection efficiency and a modification of the classical balanced link contributions property for undirected communication situations, discriminating between the roles of the nodes as head and tail.

Suggested Citation

  • Elena C. Gavilán & Conrado M. Manuel & René Van Den Brink, 2022. "A Family of Position Values for Directed Communication Situations," Mathematics, MDPI, vol. 10(8), pages 1-19, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1235-:d:790092
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    References listed on IDEAS

    as
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    2. Ghintran, Amandine, 2013. "Weighted position values," Mathematical Social Sciences, Elsevier, vol. 65(3), pages 157-163.
    3. 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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