Minimum-cost spanning tree games: Bird rule revisited

Ertan, Zhuang; Tan, Zhibin; Bai, Ye; Cao, Zhang

doi:10.1360/ssm-2020-0060

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2022

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“…This problem is called fixed tree cost-allocation problem and it has also been studied in Granot et al (1996), and Koster et al (2002) in the context of game theory. Bird's rule (Bird 1976;Ertan et al 2020) is based on a particular solution for each fixed minimum cost spanning tree of the network and then, it can also be used also for this problem. Several interesting families of rules that contain Bird's rule have been defined.…”

Section: Introductionmentioning

confidence: 99%

Cost-allocation problems for fuzzy agents in a fixed-tree network

Fernández

Gallego

Jiménez-Losada

et al. 2022

Fuzzy Optim Decis Making

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Cost-allocation problems in a fixed network are concerned with distributing the costs for use by a group of clients who cooperate in order to reduce such costs. We work only with tree networks and we assume that a minimum cost spanning tree network has already been constructed and now we are interested in the maintenance costs. The classic problem supposes that each agent stays for the entire time in the same node of the network. This paper introduces cost-allocation problems in a fixed-tree network with a set of agents whose activity over the nodes is fuzzy. Agent’s needs to pay for each period of time may differ. Moreover, the agents do not always remain in the same node for each period. We propose the extension of a very well-known solution for these problems: Bird’s rule.

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