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An Iterative Procedure for Evaluating Digraph Competitions

Listed author(s):
  • Borm, P.E.M.

    (Tilburg University, Faculty of Economics)

  • van den Brink, J.R.

    (Tilburg University, Faculty of Economics)

  • Slikker, M.

    (Tilburg University, Faculty of Economics)

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, we describe an iterative process is described which 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.

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File URL: https://pure.uvt.nl/portal/files/535117/788.pdf
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Paper provided by Tilburg University, School of Economics and Management in its series Research Memorandum with number 788.

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Date of creation: 2000
Handle: RePEc:tiu:tiurem:03637fc0-696b-4b91-b292-d0e789c88185
Contact details of provider: Web page: https://www.tilburguniversity.edu/about/schools/economics-and-management/

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  1. Laffond G. & Laslier J. F. & Le Breton M., 1993. "The Bipartisan Set of a Tournament Game," Games and Economic Behavior, Elsevier, vol. 5(1), pages 182-201, January.
  2. René van den Brink & Peter Borm, 2002. "Digraph Competitions and Cooperative Games," Theory and Decision, Springer, vol. 53(4), pages 327-342, December.
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