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arXiv · 2408.12523

Weighted Envy-Freeness in House Allocation

Sijia Dai·Yankai Chen·Xiaowei Wu·Yicheng Xu·Yong Zhang
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Abstract

The classic house allocation problem involves assigning $m$ houses to $n$ agents based on their utility functions, ensuring each agent receives exactly one house. A key criterion in these problems is satisfying fairness constraints such as envy-freeness. We extend this problem by considering agents with arbitrary weights, focusing on the concept of weighted envy-freeness, which has been extensively studied in fair division. We present a polynomial-time algorithm to determine whether weighted envy-free allocations exist and, if so, to compute one. Since weighted envy-free allocations do not always exist, we also investigate the potential of achieving such allocations through the use of subsidies. We provide several characterizations for weighted envy-freeable allocations (allocations that can be turned weighted envy-free by introducing subsidies) and show that they do not always exist, which is different from the unweighted setting. Furthermore, we explore the existence of weighted envy-freeable allocations in specific scenarios and outline the conditions under which they exist.

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Sijia Dai, Yankai Chen, Xiaowei Wu, Yicheng Xu, Yong Zhang. 2024-08-22. Weighted Envy-Freeness in House Allocation. https://arxiv.org/abs/2408.12523

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