Abstract
We consider totally connected networks of nodes forming a cluster within a broader community of agents exchanging messages. These networks are also addressed by mesh networks. We examine a scenario where the community is partitioned into multiple clusters, in each cluster one node acting as cluster head. The function of the cluster head is to send and receive messages from remote clusters while the other members within the cluster will be informed by the cluster head and can therefore keep silent in order to save resources. The way how this cluster head will be selected is an internal voting scheme based on a majority rule and preferences for all voters. The problem arises from the fact that even complete and transitive preferences of all voters on the agent set do not induce transitive collective preferences, and hence do not ensure the existence of an undominated agent, who would be a suitable candidate for a cluster head. Therefore, the selection process must become more complicated. We propose a selection procedure based on sequential voting and an assessment of nodes in the style of a Shapley Value approach. Since the weakness of the Shapley Value approach in practical applications is based on its numerical complexity, we will investigate the properties of the voting process in more detail. Moreover, we will analyze the different structures of preference schemes of the voters and establish the relationship to the Shapley value approach. This offers a numerically more tractable method for the selection of the cluster head than the calculation of the Shapley value in a straight forward way.
Published Version
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