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Connectivity and Allocation Rule in a Directed Network

Author

Listed:
  • 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
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    References listed on IDEAS

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    1. Farrell, Joseph & Gibbons, Robert, 1989. "Cheap talk can matter in bargaining," Journal of Economic Theory, Elsevier, vol. 48(1), pages 221-237, June.
    2. 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.
    3. 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.
    4. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
    5. Joseph Farrell, 1987. "Cheap Talk, Coordination, and Entry," RAND Journal of Economics, The RAND Corporation, vol. 18(1), pages 34-39, Spring.
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