Hougaard, J.L. and Tvede, M. (2022) Trouble comes in threes: core stability in minimum cost connection networks. European Journal of Operational Research, 297 (1). pp. 319-324. ISSN 0377-2217
Abstract
We consider a generalization of the Minimum Cost Spanning Tree (MCST) model, called the Minimum Cost Connection Network (MCCN) model, where network users have connection demands in the form of a pair of nodes they want connected directly or indirectly. For a fixed network, which satisfies all connection demands, the problem consists of allocating the total cost of the network among its users. Thereby every MCCN problem induces a cooperative cost game where the cost of every coalition of users is the cost of an efficient network satisfying the demand of the users in the coalition. Unlike the MCST-model, we show that the core of the induced cost game in the MCCN-model can be empty even when all locations are demanded. We therefore consider sufficient conditions for non-empty core. It is shown that: when the efficient network and the demand graph (i.e. the graph consisting of the direct connections between the pairs of demanded nodes) consist of the same components, the induced cost game has non-empty core (Theorem 1); and, when the demand graph consists of at most two components, the induced cost game has non-empty core (Theorem 2).
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2022 Elsevier. This is an author produced version of a paper subsequently published in European Journal of Operational Research. Uploaded in accordance with the publisher's self-archiving policy. Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/). |
Keywords: | Game theory; Minimum cost connection network; Spanning tree; Cost sharing; Fair allocation |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Social Sciences (Sheffield) > Department of Economics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 06 Jan 2023 14:23 |
Last Modified: | 16 Feb 2024 01:13 |
Published Version: | http://dx.doi.org/10.1016/j.ejor.2021.05.044 |
Status: | Published |
Publisher: | Elsevier BV |
Refereed: | Yes |
Identification Number: | 10.1016/j.ejor.2021.05.044 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:194800 |