Abstract
We consider the problem of fairly allocating indivisible resources to agents, which has been studied for years. Most previous work focuses on fairness and/or efficiency among agents given agents’ preferences. However, besides the agents, the allocator as the resource owner may also be involved in many real-world scenarios (e.g., government resource allocation, heritage division, company personnel assignment, etc.). The allocator has the inclination to obtain a fair or efficient allocation based on her own preference over the items and to whom each item is allocated. In this paper, we propose a new model and focus on the following two problems concerning the allocator’s fairness and efficiency:
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1.
Is it possible to find an allocation that is fair for both the agents and the allocator?
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2.
What is the complexity of maximizing the allocator’s social welfare while satisfying the agents’ fairness?
We consider the two fundamental fairness criteria: envy-freeness and proportionality. For the first problem, we study the existence of an allocation that is envy-free up to c goods (EF-c) or proportional up to c goods (PROP-c) from both the agents’ and the allocator’s perspectives, in which such an allocation is called doubly EF-c or doubly PROP-c respectively. When the allocator’s utility depends exclusively on the items (but not to whom an item is allocated), we prove that a doubly EF-1 allocation always exists. For the general setting where the allocator has a preference over the items and to whom each item is allocated, we prove that a doubly EF-1 allocation always exists for two agents, a doubly PROP-2 allocation always exists for binary valuations, and a doubly PROP-\(O(\log n)\) allocation always exists in general.
For the second problem, we provide various (in)approximability results in which the gaps between approximation and inapproximation ratios are asymptotically closed under most settings.
Most of our results are based on some novel technical tools including the chromatic numbers of the Kneser graphs and linear programming-based analysis.
The full version of this paper is available on arXiv [11]. Due to the space limit, many technical details are omitted in this version.
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Notes
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The round-robin algorithm works as follows: Given an ordering of agents, each agent picks her favorite item among the remaining items to her bundle following the ordering in rounds until there is no remaining item.
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Acknowledgment
The research of Biaoshuai Tao was supported by the National Natural Science Foundation of China (No. 62102252). The research of Shengxin Liu was partially supported by the National Natural Science Foundation of China (No. 62102117), by the Shenzhen Science and Technology Program (No. RCBS20210609103900003), and by the Guangdong Basic and Applied Basic Research Foundation (No. 2023A1515011188), and by CCF-Huawei Populus Grove Fund (No. CCF-HuaweiLK2022005).
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Bu, X., Li, Z., Liu, S., Song, J., Tao, B. (2024). Fair Division with Allocator’s Preference. In: Garg, J., Klimm, M., Kong, Y. (eds) Web and Internet Economics. WINE 2023. Lecture Notes in Computer Science, vol 14413. Springer, Cham. https://doi.org/10.1007/978-3-031-48974-7_5
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