Theory and Decision

, Volume 69, Issue 4, pp 657–669

Values for rooted-tree and sink-tree digraph games and sharing a river


DOI: 10.1007/s11238-009-9141-7

Cite this article as:
Khmelnitskaya, A.B. Theory Decis (2010) 69: 657. doi:10.1007/s11238-009-9141-7


We introduce values for rooted-tree and sink-tree digraph games axiomatically and provide their explicit formula representation. These values may be considered as natural extensions of the lower equivalent and upper equivalent solutions for line-graph games studied in van den Brink et al. (Econ Theory 33:349–349, 2007). We study the distribution of Harsanyi dividends. We show that the problem of sharing a river with a delta or with multiple sources among different agents located at different levels along the riverbed can be embedded into the framework of a rooted-tree or sink-tree digraph game correspondingly.


TU game Cooperation structure Myerson value Component efficiency Deletion link property Harsanyi dividends Sharing a river 

Copyright information

© Springer Science+Business Media, LLC. 2009

Authors and Affiliations

  1. 1.SPb Institute for Economics and Mathematics Russian Academy of SciencesSt.PetersburgRussia