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Summary: Two Solution Concepts for TU Games
with Cycle-Free Directed Cooperation Structures
Anna Khmelnitskaya1
and Dolf Talman2
1
SPb Institute for Economics and Mathematics Russian Academy of Sciences,
1 Tchaikovsky St., 191187, St.Petersburg, Russia,
E-mail: a.khmelnitskaya@math.utwente.nl
2
CentER, Department of Econometrics & Operations Research, Tilburg University,
P.O. Box 90153, 5000 LE Tilburg, The Netherlands,
E-mail: talman@uvt.nl.
Abstract. For arbitrary cycle-free directed graph games tree-type values
are introduced axiomatically and their explicit formula representation is
provided. These values may be considered as natural extensions of the tree
and sink values as has been defined correspondingly for rooted and sink for-
est graph games. The main property for the tree value is that every player
in the game receives the worth of this player together with his successors
minus what these successors receive. It implies that every coalition of players
consisting of one of the players with all his successors receives precisely its
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