English

Revisiting Fair and Efficient Allocations for Bivalued Goods

Computer Science and Game Theory 2026-04-10 v1 Data Structures and Algorithms

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.

Keywords

Cite

@article{arxiv.2604.08345,
  title  = {Revisiting Fair and Efficient Allocations for Bivalued Goods},
  author = {Hui Liu and Zhijie Zhang},
  journal= {arXiv preprint arXiv:2604.08345},
  year   = {2026}
}
R2 v1 2026-07-01T12:01:21.215Z