Connectivity and Allocation Rule in a Directed Network
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.
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Volume (Year): 8 (2008)
Issue (Month): 1 (September)
Pages: 1-21
| Handle: | RePEc:bpj:bejtec:v:8:y:2008:i:1:n:19 |
| Contact details of provider: | Web page: https://www.degruyter.com
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| Order Information: | Web: https://www.degruyter.com/view/j/bejte |
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- Farrell, Joseph & Gibbons, Robert, 1989.
"Cheap talk can matter in bargaining,"
Journal of Economic Theory,
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- Robert Gibbons & Joseph Farrell, 1988. "Cheap Talk Can Matter in Bargaining," Working papers 482, Massachusetts Institute of Technology (MIT), Department of Economics.
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- Farrell, Joseph & Gibbons, Robert, 1988. "Cheap Talk Can Matter in Bargaining," Department of Economics, Working Paper Series qt3qz786xq, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
- Slikker, Marco & Gilles, Robert P. & Norde, Henk & Tijs, Stef, 2005. "Directed networks, allocation properties and hierarchy formation," Mathematical Social Sciences, Elsevier, vol. 49(1), pages 55-80, January.
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- Joseph Farrell, 1987. "Cheap Talk, Coordination, and Entry," RAND Journal of Economics, The RAND Corporation, vol. 18(1), pages 34-39, Spring.
- Jeong-Yoo Kim, 1996. "Cheap Talk and Reputation in Repeated Pretrial Negotiation," RAND Journal of Economics, The RAND Corporation, vol. 27(4), pages 787-802, Winter. Full references (including those not matched with items on IDEAS)
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