Stable Sets in Matching Problems with Coalitional Sovereignty and Path Dominance

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

Research output: Working paperProfessional

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Abstract

We study von Neumann Morgenstern stable sets for one-to-one matching problems under the assumption of coalitional sovereignty, 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 along the lines of van Deemen (1991) and Page and Wooders (2009). This results in the pairwise myopic vNM set and the myopic vNM set, respectively. We obtain a unique prediction for both types of stable sets: the set of matchings that belong to the core. We also show that the pairwise and coalitional analogues of the level-1 farsighted set yield the core as the unique prediction.
Original languageEnglish
PublisherMaastricht University, Graduate School of Business and Economics
DOIs
Publication statusPublished - Apr 2016

Publication series

SeriesGSBE Research Memoranda
Number020

JEL classifications

  • c70 - Game Theory and Bargaining Theory: General
  • c78 - "Bargaining Theory; Matching Theory"

Keywords

  • Mathematical economics
  • Microeconomics
  • Operations research and management science

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