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Connectivity and Allocation Rule in a Directed Network

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  • Kim Jeong-Yoo

    (Kyung Hee University)

  • Jun Tackseung

    (Kyung Hee University)

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.

Suggested Citation

  • Kim Jeong-Yoo & Jun Tackseung, 2008. "Connectivity and Allocation Rule in a Directed Network," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 8(1), pages 1-21, September.
    • Handle: RePEc:bpj:bejtec:v:8:y:2008:i:1:n:19
    DOI: 10.2202/1935-1704.1465
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    References listed on IDEAS

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