Revisiting Fair and Efficient Allocations for Bivalued Goods
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910116831297536 |
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| author | Liu, Hui Zhang, Zhijie |
| author_facet | Liu, Hui Zhang, Zhijie |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08345 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Revisiting Fair and Efficient Allocations for Bivalued Goods Liu, Hui Zhang, Zhijie Computer Science and Game Theory Data Structures and Algorithms 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. |
| title | Revisiting Fair and Efficient Allocations for Bivalued Goods |
| topic | Computer Science and Game Theory Data Structures and Algorithms |
| url | https://arxiv.org/abs/2604.08345 |