2021/02/13 by Gaiane Panina, Panina, Gaiane, Rade T. Živaljević +1
Economics, Econometrics and Finance · Mathematics · #05E45 #52C99 #55M20 #91B32 #Advanced Topology and Set Theory #Combinatorics (math.CO) #Economic theories and models #FOS: Mathematics #Game Theory and Voting Systems
paper · pdf · doi:10.48550/arxiv.2102.06886
openalex publication_date 2021/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The classical approach to envy-free division and equilibrium problems 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. We illustrate the method by proving several relatives (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.