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arXiv · 2605.10802

Constant Inapproximability for Fisher Markets

Argyrios Deligkas·John Fearnley·Alexandros Hollender·Themistoklis Melissourgos
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Abstract

We study the problem of computing approximate market equilibria in Fisher markets with separable piecewise-linear concave (SPLC) utility functions. In this setting, the problem was only known to be PPAD-complete for inverse-polynomial approximations. We strengthen this result by showing PPAD-hardness for constant approximations. This means that the problem does not admit a polynomial time approximation scheme (PTAS) unless PPAD$=$P. In fact, we prove that computing any approximation better than $1/11$ is PPAD-complete. As a direct byproduct of our main result, we get the same inapproximability bound for Arrow-Debreu exchange markets with SPLC utility functions.

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BibTeXRIS

Argyrios Deligkas, John Fearnley, Alexandros Hollender, Themistoklis Melissourgos. 2026-05-11. Constant Inapproximability for Fisher Markets. https://arxiv.org/abs/2605.10802

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