Values for games with two-level communication structures

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Abstract

We consider a new model of a TU game endowed with both coalition and two-level communication structures that applies to various network situations. The approach to the value is close to that of both Myerson (1977) and Aumann and Drèze (1974): it is based on ideas of component efficiency and of one or another deletion link property, and it treats an a priori union as a self-contained unit; moreover, our approach incorporates also the idea of the Owen’s quotient game property (1977). The axiomatically introduced values possess an explicit formula representation and in many cases can be quite simply computed. The results obtained are applied to the problem of sharing an international river, possibly with a delta or multiple sources, among multiple users without international firms.
Original languageEnglish
Pages (from-to)34-50
Number of pages17
JournalDiscrete applied mathematics
Volume166
DOIs
Publication statusPublished - Mar 2014

Fingerprint

Rivers
Game
TU Game
Communication
Coalitions
Deletion
Explicit Formula
Quotient
Sharing
Union
Unit
Model
Business

Keywords

  • Owen value
  • TU game
  • Communication structure
  • Component efficiency
  • Aumann-Drèze value
  • Deletion link property
  • Myerson value
  • Coalition structure

Cite this

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title = "Values for games with two-level communication structures",
abstract = "We consider a new model of a TU game endowed with both coalition and two-level communication structures that applies to various network situations. The approach to the value is close to that of both Myerson (1977) and Aumann and Dr{\`e}ze (1974): it is based on ideas of component efficiency and of one or another deletion link property, and it treats an a priori union as a self-contained unit; moreover, our approach incorporates also the idea of the Owen’s quotient game property (1977). The axiomatically introduced values possess an explicit formula representation and in many cases can be quite simply computed. The results obtained are applied to the problem of sharing an international river, possibly with a delta or multiple sources, among multiple users without international firms.",
keywords = "Owen value, TU game, Communication structure, Component efficiency, Aumann-Dr{\`e}ze value, Deletion link property, Myerson value, Coalition structure",
author = "Khmelnitskaya, {Anna Borisovna}",
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Values for games with two-level communication structures. / Khmelnitskaya, Anna Borisovna.

In: Discrete applied mathematics, Vol. 166, 03.2014, p. 34-50.

Research output: Contribution to journalArticleAcademicpeer-review

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AB - We consider a new model of a TU game endowed with both coalition and two-level communication structures that applies to various network situations. The approach to the value is close to that of both Myerson (1977) and Aumann and Drèze (1974): it is based on ideas of component efficiency and of one or another deletion link property, and it treats an a priori union as a self-contained unit; moreover, our approach incorporates also the idea of the Owen’s quotient game property (1977). The axiomatically introduced values possess an explicit formula representation and in many cases can be quite simply computed. The results obtained are applied to the problem of sharing an international river, possibly with a delta or multiple sources, among multiple users without international firms.

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KW - Aumann-Drèze value

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