← 研踪 PaperTrailarXiv:2606.06317 · v3
Settling the Complexity of Hylland--Zeckhauser Equilibria
首次提交 2026-06-04 23:54
版本更新 2026-11-03 18:38
雷达观测 2026-11-04 23:39
摘要
The Hylland--Zeckhauser (HZ) mechanism is a foundational framework for allocating indivisible goods in one-sided matching markets via lotteries supported by competitive prices and equal artificial budgets. We resolve the exact computational complexity of the HZ scheme by proving that computing an exact HZ equilibrium is FIXP-complete, thereby settling a conjecture of Vazirani and Yannakakis. Notably, this hardness persists even when computing the equilibrium allocation alone. We establish our hardness result via a reduction that encodes quadratic fixed-point equations into a reciprocal variational inequality. On the algorithmic side, we present a deterministic polynomial-time approximation algorithm that achieves an additive error of $0.0755211 + δ$ for any $δ> 0$, significantly improving upon the previous $1/e$ guarantee.
作者备注：86 pages, 9 figure, 9 tables
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v3 · 2026-11-03 18:38 · 最新观测版本
Settling the Complexity of Hylland--Zeckhauser Equilibria
The Hylland--Zeckhauser (HZ) mechanism is a foundational framework for allocating indivisible goods in one-sided matching markets via lotteries supported by competitive prices and equal artificial budgets. We resolve the exact computational complexity of the HZ scheme by proving that computing an exact HZ equilibrium is FIXP-complete, thereby settling a conjecture of Vazirani and Yannakakis. Notably, this hardness persists even when computing the equilibrium allocation alone. We establish our hardness result via a reduction that encodes quadratic fixed-point equations into a reciprocal variational inequality. On the algorithmic side, we present a deterministic polynomial-time approximation algorithm that achieves an additive error of $0.0755211 + δ$ for any $δ> 0$, significantly improving upon the previous $1/e$ guarantee.
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