TY - UNPB

T1 - Trouble Comes in Threes

T2 - Core stability in Minimum Cost Connection Networks

AU - Hougaard, Jens Leth

AU - Tvede, Mich

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

M3 - Working paper

T3 - IFRO Working Paper

BT - Trouble Comes in Threes

PB - Department of Food and Resource Economics, University of Copenhagen

ER -