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

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 Theo...

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Bibliographic Details
Published in:Theory and decision 2010-10, Vol.69 (4), p.657-669
Main Author: Khmelnitskaya, Anna B.
Format: Article
Language:English
Subjects:
Behavioral/Experimental Economics
Communication
Cooperation
Decision making
Decision theory
Deltas
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Efficiency
Equivalence
Finance
Game Theory
Games
Insurance
Management
Operations Research/Decision Theory
Representations
Rivers
Social and Behav. Sciences
Statistics for Business
Studies
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Summary: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.
ISSN:0040-5833
1573-7187
DOI:10.1007/s11238-009-9141-7