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arXiv · 2604.08345

Revisiting Fair and Efficient Allocations for Bivalued Goods

Hui Liu·Zhijie Zhang
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Abstract

This paper re-examines the problem of fairly and efficiently allocating indivisible goods among agents with additive bivalued valuations. Garg and Murhekar (2021) proposed a polynomial-time algorithm that purported to find an EFX and fPO allocation. However, we provide a counterexample demonstrating that their algorithm may fail to terminate. To address this issue, we propose a new polynomial-time algorithm that computes a WEFX (Weighted Envy-Free up to any good) and fPO allocation, thereby correcting the prior approach and offering a more general solution. Furthermore, we show that our algorithm can be adapted to compute a WEQX (Weighted Equitable up to any good) and fPO allocation.

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Hui Liu, Zhijie Zhang. 2026-04-09. Revisiting Fair and Efficient Allocations for Bivalued Goods. https://arxiv.org/abs/2604.08345

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