Stable Sets in Matching Problems with Coalitional Sovereignity and Path Dominance

P. Jean-Jacques Herings*, Ana Mauleon, Vincent Vannetelbosch

*Corresponding author for this work

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Abstract

We study von Neumann Morgenstern stable sets for one-to-one matching problems under the assumption of coalitional sovereignty (C), meaning that a deviating coalition of players does not have the power to arrange the matches of agents outside the coalition. We study both the case of pairwise and coalitional deviations. We argue further that dominance has to be replaced by path dominance (P) along the lines of van Deemen (1991) and Page and Wooders (2009). This results in the pairwise CP vNM set in the case of pairwise deviations and the CP vNM set in the case of coalitional deviations. We obtain a unique prediction for both types of stable sets: the set of matchings that belong to the core. (C) 2017 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)14-19
Number of pages6
JournalJournal of Mathematical Economics
Volume71
Issue numberAugust 2017
DOIs
Publication statusPublished - Aug 2017

Keywords

  • Matching problems
  • Stable sets
  • Enforceability
  • Coalitional sovereignty
  • Path dominance
  • FARSIGHTED STABILITY
  • GAMES
  • CORE

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