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

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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.

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Authors and Affiliations

  1. SPb Institute for Economics and Mathematics Russian Academy of Sciences, 1 Tchaikovsky St., 191187, St.Petersburg, Russia

    Anna B. Khmelnitskaya

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  1. Anna B. Khmelnitskaya
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Correspondence to Anna B. Khmelnitskaya.

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Khmelnitskaya, A.B. Values for rooted-tree and sink-tree digraph games and sharing a river. Theory Decis 69, 657–669 (2010). https://doi.org/10.1007/s11238-009-9141-7

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  • DOI: https://doi.org/10.1007/s11238-009-9141-7

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