Digraph Competitions and Cooperative Games

J.R. van den Brink; P. Borm

doi:10.1023/A:1024162419357

Digraph Competitions and Cooperative Games

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Abstract

Digraph games are cooperative TU-games associated to domination structures which can be modeled by directed graphs. Examples come from sports competitions or from simple majority win digraphs corresponding to preference profiles in social choice theory. The Shapley value, core, marginal vectors and selectope vectors of digraph games are characterized in terms of so-called simple score vectors. A general characterization of the class of (almost positive) TU-games where each selectope vector is a marginal vector is provided in terms of game semi-circuits. Finally, applications to the ranking of teams in sports competitions and of alternatives in social choice theory are discussed.

Original language	English
Pages (from-to)	327-342
Number of pages	15
Journal	Theory and Decision
Volume	53
DOIs	https://doi.org/10.1023/A:1024162419357
Publication status	Published - 2002

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title = "Digraph Competitions and Cooperative Games",

abstract = "Digraph games are cooperative TU-games associated to domination structures which can be modeled by directed graphs. Examples come from sports competitions or from simple majority win digraphs corresponding to preference profiles in social choice theory. The Shapley value, core, marginal vectors and selectope vectors of digraph games are characterized in terms of so-called simple score vectors. A general characterization of the class of (almost positive) TU-games where each selectope vector is a marginal vector is provided in terms of game semi-circuits. Finally, applications to the ranking of teams in sports competitions and of alternatives in social choice theory are discussed.",

author = "{van den Brink}, J.R. and P. Borm",

year = "2002",

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AU - Borm, P.

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AB - Digraph games are cooperative TU-games associated to domination structures which can be modeled by directed graphs. Examples come from sports competitions or from simple majority win digraphs corresponding to preference profiles in social choice theory. The Shapley value, core, marginal vectors and selectope vectors of digraph games are characterized in terms of so-called simple score vectors. A general characterization of the class of (almost positive) TU-games where each selectope vector is a marginal vector is provided in terms of game semi-circuits. Finally, applications to the ranking of teams in sports competitions and of alternatives in social choice theory are discussed.

U2 - 10.1023/A:1024162419357

DO - 10.1023/A:1024162419357

M3 - Article

SN - 0040-5833

VL - 53

SP - 327

EP - 342

JO - Theory and Decision

JF - Theory and Decision

ER -

Digraph Competitions and Cooperative Games

Abstract

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