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Maximizing Social Welfare Among EF1 Allocations at the Presence of Two Types of Agents

Authors Jiaxuan Ma, Yong Chen , Guangting Chen , Mingyang Gong , Guohui Lin , An Zhang

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ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Fair allocation
  • utilitarian social welfare
  • envy-free up to one item
  • envy-cycle elimination
  • round robin
  • approximation algorithm

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Abstract

We study the fair allocation of indivisible items to n agents to maximize the utilitarian social welfare, where the fairness criterion is envy-free up to one item and there are only two different utility functions shared by the agents. We present a 2-approximation algorithm when the two utility functions are normalized, improving the previous best ratio of 16 √n shown for general normalized utility functions; thus this constant ratio approximation algorithm confirms the APX-completeness in this special case previously shown APX-hard. When there are only three agents, i.e., n = 3, the previous best ratio is 3 shown for general utility functions, and we present an improved and tight 5/3-approximation algorithm when the two utility functions are normalized, and a best possible and tight 2-approximation algorithm when the two utility functions are unnormalized.

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Jiaxuan Ma, Yong Chen, Guangting Chen, Mingyang Gong, Guohui Lin, and An Zhang. Maximizing Social Welfare Among EF1 Allocations at the Presence of Two Types of Agents. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 49:1-49:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ISAAC.2025.49

Author Details

Jiaxuan Ma
  • Hangzhou Dianzi University, China
Yong Chen
  • Hangzhou Dianzi University, China
Guangting Chen
  • Zhejiang University of Water Resources and Electric Power, Hangzhou, China
Mingyang Gong
  • University of Alberta, Edmonton, Canada
Guohui Lin
  • University of Alberta, Edmonton, Canada
An Zhang
  • Hangzhou Dianzi University, China

Funding

Supported by the NSERC Canada, the NNSF of China (Grants 12471301, 12371316), the PNSF of Zhejiang China (Grant LZ25A010001), and the China Scholarship Council (Grant No. 202508330173).

References

  1. G. Amanatidis, H. Aziz, G. Birmpas, A. Filos-Ratsikas, B. Li, H. Moulin, A. A. Voudouris, and X. Wu. Fair division of indivisible goods: Recent progress and open questions. Artificial Intelligence, 322:Article 103965, 2023. Google Scholar
  2. G. Amanatidis, G. Birmpas, A. Filos-Ratsikas, and A. Voudouris. Fair division of indivisible goods: A survey. In Proceedings of IJCAI 2022, pages 5385-5393, 2022. Google Scholar
  3. H. Aziz, X. Huang, N. Mattei, and E. Segal-Halevi. Computing welfare-maximizing fair allocations of indivisible goods. European Journal of Operational Research, 307:773-784, 2023. URL: https://doi.org/10.1016/J.EJOR.2022.10.013.
  4. S. Barman, U. Bhaskar, and N. Shah. Optimal bounds on the price of fairness for indivisible goods. In Proceedings of WINE 2020, pages 356-369, 2020. Google Scholar
  5. X. Bei, X. Lu, P. Manurangesi, and W. Suksompong. The price of fairness for indivisible goods. Theory of Computing Systems, 65:1069-1093, 2021. URL: https://doi.org/10.1007/S00224-021-10039-8.
  6. X. Bu, Z. Li, S. Liu, J. Song, and B. Tao. Approximability landscape of welfare maximization within fair allocations. In Proceedings of EC 2025, pages 412-440, 2025. Google Scholar
  7. E. Budish. The combinatorial assignment problem: Approximate competitive equilibrium from equal incomes. Journal of Political Economy, 119:1061-1103, 2011. Google Scholar
  8. I. Caragiannis, D. Kurokawa, H. Moulin, A. Procaccia, N. Shah, and J. Wang. The unreasonable fairness of maximum Nash welfare. ACM Transactions on Economics and Computation, 7:12:1-12:32, 2019. URL: https://doi.org/10.1145/3355902.
  9. R. Lipton, E. Markakis, E. Mossel, and A. Saberi. On approximately fair allocations of indivisible goods. In Proceedings of EC 2004, pages 125-131, 2004. Google Scholar
  10. J. Ma, Y. Chen, G. Chen, M. Gong, G. Lin, and A. Zhang. Maximizing social welfare among EF1 allocations at the presence of two types of agents. CoRR, 2025. URL: https://arxiv.org/abs/2509.09641.
  11. H. Steinhaus. Sur la division pragmatique. Econometrica, 17:315-319, 1949. Google Scholar
  12. H. Varian. Equity, envy and efficiency. Journal of Economic Theory, 9:63-91, 1974. Google Scholar
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