A BEJTE Contributions article.

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.

Submitted: March 5, 2008 · Accepted: July 17, 2008 · Published: September 3, 2008

Recommended Citation

Kim, Jeong-Yoo and Jun, Tackseung (2008) "Connectivity and Allocation Rule in a Directed Network," The B.E. Journal of Theoretical Economics: Vol. 8 : Iss. 1 (Contributions), Article 19.
Available at: http://www.bepress.com/bejte/vol8/iss1/art19