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An iterative procedure for evaluating digraph competitions

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Author Info
Borm, P.
Brink, R. van den
Slikker, M. (Tilburg University, Faculty of Economics and Business Administration)

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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, 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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Publisher Info
Paper provided by Tilburg University, Faculty of Economics and Business Administration in its series Research Memorandum with number 788.

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Date of creation: 2000
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Handle: RePEc:dgr:kubrem:2000788

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Related research
Keywords: digraph competitions;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  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. [Downloadable!] (restricted)
  2. René van den Brink & Peter Borm, 2002. "Digraph Competitions and Cooperative Games," Theory and Decision, Springer, vol. 53(4), pages 327-342, December. [Downloadable!] (restricted)
  3. Borm, Peter & van den Brink, Rene & Levinsky, Rene & Slikker, Marco, 2004. "On two new social choice correspondences," Mathematical Social Sciences, Elsevier, vol. 47(1), pages 51-68, January. [Downloadable!] (restricted)
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  1. Quant, M. & Borm, P. & Reijnierse, H. & Voorneveld, M., 2002. "Characterizations of solutions in digraph competitions," Discussion Paper 113, Tilburg University, Center for Economic Research. [Downloadable!]
  2. Yuan Ju & Peter Borm & Pieter Ruys, 2007. "The consensus value: a new solution concept for cooperative games," Social Choice and Welfare, Springer, vol. 28(4), pages 685-703, June. [Downloadable!] (restricted)
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  3. René Brink & Peter Borm & Ruud Hendrickx & Guillermo Owen, 2008. "Characterizations of the β- and the Degree Network Power Measure," Theory and Decision, Springer, vol. 64(4), pages 519-536, June. [Downloadable!] (restricted)
  4. René van den Brink & Peter Borm & Ruud Hendrickx & Guillermo Owen, 2005. "Characterizations of Network Power Measures," Tinbergen Institute Discussion Papers 05-061/1, Tinbergen Institute. [Downloadable!]
  5. Herings, P.J.J. & Laan, G. van der & Talman, D., 2001. "Measuring the power of nodes in digraphs," Discussion Paper 72, Tilburg University, Center for Economic Research. [Downloadable!]
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