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arXiv · 2102.06886

Envy-free division via configuration spaces

Gaiane Panina·Rade Živaljević
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Abstract

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.

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Gaiane Panina, Rade Živaljević. 2021-03-18. Envy-free division via configuration spaces. https://arxiv.org/abs/2102.06886

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