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arXiv · 2107.05746

Computational Hardness of the Hylland-Zeckhauser Scheme

Thomas Chen·Xi Chen·Binghui Peng·Mihalis Yannakakis
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Abstract

We study the complexity of the classic Hylland-Zeckhauser scheme [HZ'79] for one-sided matching markets. We show that the problem of finding an $ε$-approximate equilibrium in the HZ scheme is PPAD-hard, and this holds even when $ε$ is polynomially small and when each agent has no more than four distinct utility values. Our hardness result, when combined with the PPAD membership result of [VY'21], resolves the approximation complexity of the HZ scheme. We also show that the problem of approximating the optimal social welfare (the weight of the matching) achievable by HZ equilibria within a certain constant factor is NP-hard.

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Thomas Chen, Xi Chen, Binghui Peng, Mihalis Yannakakis. 2021-07-12. Computational Hardness of the Hylland-Zeckhauser Scheme. https://arxiv.org/abs/2107.05746

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