The average covering tree value for directed graph games

Anna Khmelnitskaya*, Özer Selcuk, Dolf Talman

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)
2 Downloads (Pure)

Abstract

We introduce a single-valued solution concept, the so-called average covering tree value, for the class of transferable utility games with limited communication structure represented by a directed graph. The solution is the average of the marginal contribution vectors corresponding to all covering trees of the directed graph. The covering trees of a directed graph are those (rooted) trees on the set of players that preserve the dominance relations between the players prescribed by the directed graph. The average covering tree value is component efficient, and under a particular convexity-type condition it is stable. For transferable utility games with complete communication structure the average covering tree value equals to the Shapley value of the game. If the graph is the directed analog of an undirected graph the average covering tree value coincides with the gravity center solution.
Original languageEnglish
Pages (from-to)315-333
Number of pages19
JournalJournal of combinatorial optimization
Volume39
Issue number2
Early online date30 Nov 2019
DOIs
Publication statusPublished - 1 Feb 2020
Externally publishedYes

Keywords

  • UT-Hybrid-D
  • Directed communication structure
  • Marginal contribution vector
  • Myerson value
  • Average tree solution
  • · Stability
  • TU game

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