Description

• Title:
  Envy-free division via configuration spaces
• Creator:
  Panina, Gaiane;
  Živaljević, Rade T.
• Description:
  The classical approach to envy-free division and equilibrium problems arising in mathematical economics typically relies on Knaster-Kuratowski-Mazurkiewicz theorem, Sperner's lemma or some extension involving mapping degree. We propose a different and relatively novel approach where the emphasis is on configuration spaces and equivariant topology, originally developed for applications in discrete and computational geometry (Tverberg type problems, necklace splitting problem, etc.). We illustrate the method by proving several counterparts and extensions of the classical envy-free division theorem of David Gale, where the emphasis is on preferences allowing the players to choose degenerate pieces of the cake.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nd/4.0 ;
  Prawa autorskie (c) 2023 Gaiane Panina, Rade T. Živaljević
• Date:
  2023.02.26
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 61, No 1 (March 2023); 83 - 106;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/42815/34972 ;https://apcz.umk.pl/TMNA/article/view/42815/34973
• Subject:
  Envy-free division;
  configuration space/test map scheme;
  Primary: 91B32, 55M20;
  Secondary: 05E45
• Identifier: https://apcz.umk.pl/TMNA/article/view/42815
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other