An Iterative Procedure for Evaluating Digraph Competitions

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

Research output: Book/ReportReportProfessional

232 Downloads (Pure)

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.
Original languageEnglish
Place of PublicationTilburg
PublisherMicroeconomics
Number of pages17
Volume788
Publication statusPublished - 2000

Publication series

NameFEW Research Memorandum
Volume788

Keywords

  • cooperative games
  • stochastic processes
  • iterative methods
  • digraph competitions

Cite this

Borm, P. E. M., van den Brink, J. R., & Slikker, M. (2000). An Iterative Procedure for Evaluating Digraph Competitions. (FEW Research Memorandum; Vol. 788). Tilburg: Microeconomics.
Borm, P.E.M. ; van den Brink, J.R. ; Slikker, M. / An Iterative Procedure for Evaluating Digraph Competitions. Tilburg : Microeconomics, 2000. 17 p. (FEW Research Memorandum).
@book{03637fc0696b4b91b292d0e789c88185,
title = "An Iterative Procedure for Evaluating Digraph Competitions",
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.",
keywords = "cooperative games, stochastic processes, iterative methods, digraph competitions",
author = "P.E.M. Borm and {van den Brink}, J.R. and M. Slikker",
note = "Pagination: 17",
year = "2000",
language = "English",
volume = "788",
series = "FEW Research Memorandum",
publisher = "Microeconomics",

}

Borm, PEM, van den Brink, JR & Slikker, M 2000, An Iterative Procedure for Evaluating Digraph Competitions. FEW Research Memorandum, vol. 788, vol. 788, Microeconomics, Tilburg.

An Iterative Procedure for Evaluating Digraph Competitions. / Borm, P.E.M.; van den Brink, J.R.; Slikker, M.

Tilburg : Microeconomics, 2000. 17 p. (FEW Research Memorandum; Vol. 788).

Research output: Book/ReportReportProfessional

TY - BOOK

T1 - An Iterative Procedure for Evaluating Digraph Competitions

AU - Borm, P.E.M.

AU - van den Brink, J.R.

AU - Slikker, M.

N1 - Pagination: 17

PY - 2000

Y1 - 2000

N2 - 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.

AB - 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.

KW - cooperative games

KW - stochastic processes

KW - iterative methods

KW - digraph competitions

M3 - Report

VL - 788

T3 - FEW Research Memorandum

BT - An Iterative Procedure for Evaluating Digraph Competitions

PB - Microeconomics

CY - Tilburg

ER -

Borm PEM, van den Brink JR, Slikker M. An Iterative Procedure for Evaluating Digraph Competitions. Tilburg: Microeconomics, 2000. 17 p. (FEW Research Memorandum).