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An Iterative Procedure for Evaluating Digraph Competitions

Listed author(s):
  • Peter Borm

    ()

  • René van den Brink
  • Marco Slikker

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. Copyright Kluwer Academic Publishers 2002

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File URL: http://hdl.handle.net/10.1023/A:1016339832755
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Article provided by Springer in its journal Annals of Operations Research.

Volume (Year): 109 (2002)
Issue (Month): 1 (January)
Pages: 61-75

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Handle: RePEc:spr:annopr:v:109:y:2002:i:1:p:61-75:10.1023/a:1016339832755
DOI: 10.1023/A:1016339832755
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  1. René van den Brink & Peter Borm, 2002. "Digraph Competitions and Cooperative Games," Theory and Decision, Springer, vol. 53(4), pages 327-342, December.
  2. 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.
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