A Family of Position Values for Directed Communication Situations

Elena C. Gavilán, Conrado M. Manuel*, René van den Brink

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

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.

Original languageEnglish
Article number1235
Pages (from-to)1-19
Number of pages19
JournalMathematics
Volume10
Issue number8
Early online date9 Apr 2022
DOIs
Publication statusPublished - Apr 2022

Bibliographical note

Funding Information:
This research has been partially supported by the ?Plan Nacional de I+D+i? of the Spanish Government under the project PID2020-116884GB-I00.

Publisher Copyright:
© 2022 by the authors. Licensee MDPI, Basel, Switzerland.

Keywords

  • axiomatizations
  • cooperative TU game
  • directed communication
  • directed graph
  • position value

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