The covering values for acyclic digraph games

The covering values for acyclic digraph games

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Article ID: iaor201110526
Volume: 40
Issue: 4
Start Page Number: 697
End Page Number: 718
Publication Date: Nov 2011
Journal: International Journal of Game Theory
Authors: ,
Keywords: graphs
Abstract:

We introduce a novel covering method to compute values for acyclic digraph games, and we call the values obtained by this method the covering values. These values may be considered as natural extensions of the component efficient solutions for line-graph games studied by van den Brink et al. (2007), and the tree values studied by Khmelnitskaya (2010a). With the new method, we reinterpret the tree values proposed by Khmelnitskaya (2010a). Besides, we propose the covering values in the digraph game with general acyclic digraph structures presenting flow situations when some links may merge while others split into several separate ones. We give axiomatizations of these values, and interpret these values in terms of dividend distributions.

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