The average covering tree value for directed graph games

Anna Khmelnitskaya, Özer Selçuk, Dolf Talman

Research output

1 Citation (Scopus)


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
JournalJournal of Combinatorial Optimization
Issue number2
Early online date30 Nov 2019
Publication statusPublished - 1 Feb 2020


Scopus subject areas

  • Control and Optimization
  • Applied Mathematics
  • Discrete Mathematics and Combinatorics
  • Computer Science Applications
  • Computational Theory and Mathematics

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