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Trouble Comes in Threes: Core stability in Minimum Cost Connection Networks

Jens Hougaard () and Mich Tvede ()
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Mich Tvede: University of East Anglia

No 2020/07, IFRO Working Paper from University of Copenhagen, Department of Food and Resource Economics

Abstract: We consider a generalization of the Minimum Cost Spanning Tree (MCST) model dubbed the Minimum Cost Connection Network (MCCN) model, where network users have connection demands in the form of a pair of target nodes they want connected directly, or indirectly. Given a network which satisfies all connection demands at min-imum cost, the problem consists of allocating the total cost of the efficient network among its users. As such, every MCCN problem induces a cooperative cost game where the cost of each each coalition of users is given by the cost of an efficient net-work satisfying the demand of the users in the coalition. Unlike in the MCST model we show that the core of the induced cost game in the MCCN model can be empty (without introducing Steiner nodes). We therefore consider sufficient conditions for non-empty core. Theorem 1 shows that when the efficient network and the demand graph consist of the same components, the induced cost game has non-empty core. Theorem 2 shows that when the demand graph has at most two components the induced cost game has non-empty core.

Keywords: Minimum Cost Connection Network; Minimum Cost Spanning Tree; Cost Sharing; Fair allocation; The core; Balanced games (search for similar items in EconPapers)
JEL-codes: C70 C72 D71 D85 (search for similar items in EconPapers)
Pages: 12 pages
Date: 2020-07
New Economics Papers: this item is included in nep-gth and nep-net
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