Connectivity and Allocation Rule in a Directed Network

Jeong-Yoo Kim and Jun Tackseung
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Jun Tackseung: Kyung Hee University, tj32gm@gmail.com

The B.E. Journal of Theoretical Economics, 2008, vol. 8, issue 1, 21

Abstract: We introduce a new notion of connectivity, what we call weak connectivity, in a directed network where communication is one-way, and show that weak connectivity is equivalent to the usual concept of connectivity if the outdegree of each node is at most one, referred as the [DC] condition. Based on weak connectivity, we define an allocation rule in a directed network by applying the Shapley value type of consideration. We show that the allocation rule is the unique allocation rule satisfying component efficiency and equal bargaining power under the [DC] condition. If the [DC] condition does not hold, it fails to satisfy component efficiency, but can be shown to be the only allocation rule that satisfies equal bargaining power and quasi-component efficiency which is a weaker property.

Keywords: allocation rule; directed network; Myerson value; quasi-component efficiency; weak connectivity (search for similar items in EconPapers)
Date: 2008
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DOI: 10.2202/1935-1704.1465

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