### 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 language | English |
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Place of Publication | Tilburg |

Publisher | Microeconomics |

Number of pages | 17 |

Volume | 788 |

Publication status | Published - 2000 |

### Publication series

Name | FEW Research Memorandum |
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Volume | 788 |

### Keywords

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

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## 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). Microeconomics.