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.
| Original language | English |
|---|---|
| Article number | 19 |
| Journal | B.E. Journal of Theoretical Economics |
| Volume | 8 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2008 |
Bibliographical note
Funding Information:KEYWORDS: allocation rule, directed network, Myerson value, quasi-component efficiency, weak connectivity ∗We are thankful to seminar audiences at POSTECH, KAIST (Korea Advanced Institute of Science and Technology), KFAS (Korea Foundation of Advanced Studies) and the 2007 Far Eastern Econometric Society Meeting held in Taiwan for helpful comments.
Keywords
- Allocation rule
- Directed network
- Myerson value
- Quasi-component efficiency
- Weak connectivity