Theory and Decision

, Volume 69, Issue 4, pp 657–669 | Cite as

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

Article

Abstract

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.

Keywords

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

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References

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Copyright information

© Springer Science+Business Media, LLC. 2009

Authors and Affiliations

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

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