## Trouble comes in threes: Core stability in minimum cost connection networks

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**Trouble comes in threes : Core stability in minimum cost connection networks.** / Hougaard, Jens Leth; Tvede, Mich.

Research output: Contribution to journal › Journal article › Research › peer-review

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*European Journal of Operational Research*, vol. 297, no. 1, pp. 319-324. https://doi.org/10.1016/j.ejor.2021.05.044

#### APA

*European Journal of Operational Research*,

*297*(1), 319-324. https://doi.org/10.1016/j.ejor.2021.05.044

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#### RIS

TY - JOUR

T1 - Trouble comes in threes

T2 - Core stability in minimum cost connection networks

AU - Hougaard, Jens Leth

AU - Tvede, Mich

PY - 2022

Y1 - 2022

N2 - 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).

AB - 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).

U2 - 10.1016/j.ejor.2021.05.044

DO - 10.1016/j.ejor.2021.05.044

M3 - Journal article

VL - 297

SP - 319

EP - 324

JO - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

IS - 1

ER -

ID: 271693294