The Nucleolus and Inheritance of Properties in Communication Situations

Jop Schouten, Bas Dietzenbacher, Peter Borm

Research output: Working paperDiscussion paperOther research output

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Abstract

This paper studies the nucleolus of graph-restricted games as an alternative for the Shapley value to evaluate communication situations. We focus on the inheritance of properties of cooperative games related to the nucleolus: balancedness (the nucleolus is in the core), compromise stability and strong compromise admissibility (these properties allow for a direct, closed formula for the nucleolus). We characterize the families of graphs for which the graph-restricted games inherit these properties from the underlying games. Moreover,
for each of these properties, we characterize the family of graphs for which the nucleolus is invariant.
Original languageEnglish
Place of PublicationTilburg
PublisherCentER, Center for Economic Research
Number of pages19
Volume2019-008
Publication statusPublished - 20 Mar 2019

Publication series

NameCentER Discussion Paper
Volume2019-008

Fingerprint

Nucleolus
Game
Graph in graph theory
Balancedness
Shapley Value
Cooperative Game
Admissibility
Communication
Closed
Invariant
Evaluate
Alternatives

Keywords

  • nucleolus
  • communication situations
  • graph-restricted game
  • inheritance of properties
  • compormise stability
  • strong compromise admissibility
  • invariance

Cite this

Schouten, J., Dietzenbacher, B., & Borm, P. (2019). The Nucleolus and Inheritance of Properties in Communication Situations. (CentER Discussion Paper; Vol. 2019-008). Tilburg: CentER, Center for Economic Research.
Schouten, Jop ; Dietzenbacher, Bas ; Borm, Peter. / The Nucleolus and Inheritance of Properties in Communication Situations. Tilburg : CentER, Center for Economic Research, 2019. (CentER Discussion Paper).
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Schouten, J, Dietzenbacher, B & Borm, P 2019 'The Nucleolus and Inheritance of Properties in Communication Situations' CentER Discussion Paper, vol. 2019-008, CentER, Center for Economic Research, Tilburg.

The Nucleolus and Inheritance of Properties in Communication Situations. / Schouten, Jop; Dietzenbacher, Bas; Borm, Peter.

Tilburg : CentER, Center for Economic Research, 2019. (CentER Discussion Paper; Vol. 2019-008).

Research output: Working paperDiscussion paperOther research output

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T1 - The Nucleolus and Inheritance of Properties in Communication Situations

AU - Schouten, Jop

AU - Dietzenbacher, Bas

AU - Borm, Peter

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N2 - This paper studies the nucleolus of graph-restricted games as an alternative for the Shapley value to evaluate communication situations. We focus on the inheritance of properties of cooperative games related to the nucleolus: balancedness (the nucleolus is in the core), compromise stability and strong compromise admissibility (these properties allow for a direct, closed formula for the nucleolus). We characterize the families of graphs for which the graph-restricted games inherit these properties from the underlying games. Moreover,for each of these properties, we characterize the family of graphs for which the nucleolus is invariant.

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KW - compormise stability

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KW - invariance

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Schouten J, Dietzenbacher B, Borm P. The Nucleolus and Inheritance of Properties in Communication Situations. Tilburg: CentER, Center for Economic Research. 2019 Mar 20. (CentER Discussion Paper).