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Connectivity and Allocation Rule in a Directed Network
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Jeong-Yoo Kim
Published/Copyright:
September 3, 2008
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.
Keywords: allocation rule; directed network; Myerson value; quasi-component efficiency; weak connectivity
Published Online: 2008-9-3
©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston
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Keywords for this article
allocation rule;
directed network;
Myerson value;
quasi-component efficiency;
weak connectivity
Articles in the same Issue
- Topics Article
- When Stackelberg and Cournot Equilibria Coincide
- Conflict and Consensus: A Theory of Control in Organisations
- Backward Integrated Information Gatekeepers and Independent Divisions in the Product Market
- Identification of Individual Demands from Market Data under Uncertainty
- On the Role of Uncertainty in the Risk-Incentives Tradeoff
- Time-to-Build and the Inverse U-Shape Investment-Uncertainty Relationship
- Revisiting Independence and Stochastic Dominance for Compound Lotteries
- On Competitive Equilibria with Asymmetric Information
- A Duopoly Location Toolkit: Consumer Densities Which Yield Unique Spatial Duopoly Equilibria
- Purchasing Power Parity with Strategic Markets
- Global vs. Local Information in (Anti-)Coordination Problems with Imitators
- Costly Evidence Production and the Limits of Verifiability
- Research Joint Ventures, Optimal Licensing, and the R&D Subsidy Policy
- Comparative Statics and Welfare in Heterogeneous All-Pay Auctions: Bribes, Caps, and Performance Thresholds
- Ex Post Private Information and Monopolistic Screening
- Passing the Buck in Sequential Negotiation
- Bidding Strategies for Simultaneous Ascending Auctions
- The Dirty Face Problem with Unawareness
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