An iterative procedure for evaluating digraph competitions

P. Borm, J.R. van den Brink, M. Slikker

    Research output: Contribution to JournalArticleAcademic

    Abstract

    A competition which is based on the results of (partial) pairwise comparisons can be modelled by means of a directed graph. Given initial weights on the nodes in such digraph competitions, we view the measurement of the importance (i.e., the cardinal ranking) of the nodes as an allocation problem where we redistribute the initial weights on the basis of insights from cooperative game theory. After describing the resulting procedure of redistributing the initial weights, an iterative process is described that repeats this procedure: at each step the allocation obtained in the previous step determines the new input weights. Existence and uniqueness of the limit is established for arbitrary digraphs. Applications to the evaluation of, e.g., sport competitions and paired comparison experiments are discussed.
    Original languageEnglish
    Pages (from-to)61-75
    Number of pages14
    JournalAnnals of Operations Research
    Volume109
    DOIs
    Publication statusPublished - 2002

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