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The Long Arm of Nashian Allocation in Online p-Mean Welfare Maximization

Authors Zhiyi Huang , Chui Shan Lee , Xinkai Shu , Zhaozi Wang

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  • Theory of computation → Online algorithms
Keywords
  • Online Algorithms
  • Fair Division
  • Nash Welfare

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Abstract

We study the online allocation of divisible items to n agents with additive valuations for p-mean welfare maximization, a problem introduced by Barman, Khan, and Maiti (2022). Our algorithmic and hardness results characterize the optimal competitive ratios for the entire spectrum of -∞ ≤ p ≤ 1. Surprisingly, our improved algorithms for all p ≤ (1)/(log n) are simply the greedy algorithm for the Nash welfare, supplemented with two auxiliary components to ensure all agents have non-zero utilities and to help a small number of agents with low utilities. In this sense, the long arm of Nashian allocation achieves near-optimal competitive ratios not only for Nash welfare but also all the way to egalitarian welfare.

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Zhiyi Huang, Chui Shan Lee, Xinkai Shu, and Zhaozi Wang. The Long Arm of Nashian Allocation in Online p-Mean Welfare Maximization. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 98:1-98:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.98

Author Details

Zhiyi Huang
  • The University of Hong Kong, Pokfulam, Hong Kong
Chui Shan Lee
  • The University of Hong Kong, Pokfulam, Hong Kong
Xinkai Shu
  • Max Planck Institute for Informatics, Saarbrücken, Germany
Zhaozi Wang
  • New York University, NY, US

Funding

  • Huang, Zhiyi: This work is supported by NSFC (No. 6212290003).

References

  1. Martin Aleksandrov, Haris Aziz, Serge Gaspers, and Toby Walsh. Online fair division: analysing a food bank problem. In Proceedings of the 24th International Joint Conference on Artificial Intelligence, pages 2540-2546, 2015. URL: https://doi.org/10.5555/2832581.2832604.
  2. Martin Aleksandrov and Toby Walsh. Online fair division: A survey. In Proceedings of the 34th AAAI Conference on Artificial Intelligence, pages 13557-13562, 2020. URL: https://doi.org/10.1609/aaai.v34i09.7081.
  3. Noga Alon, Baruch Awerbuch, Yossi Azar, Niv Buchbinder, and Joseph Naor. A general approach to online network optimization problems. ACM Transactions on Algorithms, 2(4):640-660, 2006. URL: https://doi.org/10.1145/1198513.1198522.
  4. Siddhartha Banerjee, Vasilis Gkatzelis, Artur Gorokh, and Billy Jin. Online Nash social welfare maximization with predictions. In Proceedings of the 33rd Annual ACM-SIAM Symposium on Discrete Algorithms, pages 1-19. SIAM, 2022. URL: https://doi.org/10.1137/1.9781611977073.1.
  5. Siddhartha Banerjee, Vasilis Gkatzelis, Safwan Hossain, Billy Jin, Evi Micha, and Nisarg Shah. Proportionally fair online allocation of public goods with predictions. In Proceedings of the 32nd International Joint Conference on Artificial Intelligence, pages 20-28, 2023. URL: https://doi.org/10.24963/ijcai.2023/3.
  6. Nikhil Bansal and Maxim Sviridenko. The santa claus problem. In Proceedings of the 38th Annual ACM Symposium on Theory of Computing, pages 31-40, 2006. URL: https://doi.org/10.1145/1132516.1132522.
  7. Siddharth Barman, Umang Bhaskar, Anand Krishna, and Ranjani G Sundaram. Tight approximation algorithms for p-mean welfare under subadditive valuations. In Proceedings of the 28th Annual European Symposium on Algorithms, pages 11:1-11:17, 2020. URL: https://doi.org/10.4230/LIPIcs.ESA.2020.11.
  8. Siddharth Barman, Arindam Khan, and Arnab Maiti. Universal and tight online algorithms for generalized-mean welfare. In Proceedings of the 36th AAAI Conference on Artificial Intelligence, pages 4793-4800, 2022. URL: https://doi.org/10.1609/aaai.v36i5.20406.
  9. Siddharth Barman, Sanath Kumar Krishnamurthy, and Rohit Vaish. Finding fair and efficient allocations. In Proceedings of the 19th ACM Conference on Economics and Computation, pages 557-574, 2018. URL: https://doi.org/10.1145/3219166.3219176.
  10. Gerdus Benadè, Aleksandr M Kazachkov, Ariel D Procaccia, and Christos-Alexandros Psomas. How to make envy vanish over time. In Proceedings of the 19th ACM Conference on Economics and Computation, pages 593-610, 2018. URL: https://doi.org/10.1145/3219166.3219179.
  11. Ivona Bezáková and Varsha Dani. Allocating indivisible goods. ACM SIGecom Exchanges, 5(3):11-18, 2005. URL: https://doi.org/10.1145/1120680.1120683.
  12. Niv Buchbinder and Joseph Naor. Online primal-dual algorithms for covering and packing. Mathematics of Operations Research, 34(2):270-286, 2009. URL: https://doi.org/10.1287/moor.1080.0363.
  13. Ioannis Caragiannis, David Kurokawa, Hervé Moulin, Ariel Procaccia, Nisarg Shah, and Junxing Wang. The unreasonable fairness of maximum nash welfare. ACM Transactions on Economics and Computation, 7(3):1-32, 2019. URL: https://doi.org/10.1145/3355902.
  14. Deeparnab Chakrabarty, Julia Chuzhoy, and Sanjeev Khanna. On allocating goods to maximize fairness. In Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science, pages 107-116, 2009. URL: https://doi.org/10.1109/FOCS.2009.51.
  15. Bhaskar Ray Chaudhury, Jugal Garg, and Ruta Mehta. Fair and efficient allocations under subadditive valuations. In Proceedings of the 35th AAAI Conference on Artificial Intelligence, pages 5269-5276, 2021. URL: https://doi.org/10.1609/aaai.v35i6.16665.
  16. Ilan Reuven Cohen and Debmalya Panigrahi. A general framework for learning-augmented online allocation. In Proceedings of the 50th International Colloquium on Automata, Languages, and Programming, pages 43:1-43:21, 2023. URL: https://doi.org/10.4230/LIPIcs.ICALP.2023.43.
  17. Nikhil R Devanur and Kamal Jain. Online matching with concave returns. In Proceedings of the 44th Annual ACM Symposium on Theory of Computing, pages 137-144, 2012. URL: https://doi.org/10.1145/2213977.2213992.
  18. Shahar Dobzinski, Wenzheng Li, Aviad Rubinstein, and Jan Vondrák. A constant-factor approximation for nash social welfare with subadditive valuations. In Proceedings of the 56th Annual ACM Symposium on Theory of Computing, pages 467-478, 2024. URL: https://doi.org/10.1145/3618260.3649740.
  19. Yuda Feng and Shi Li. A note on approximating weighted nash social welfare with additive valuations. In Proceedings of the 51st EATCS International Colloquium on Automata, Languages and Programming, 2024. URL: https://doi.org/10.4230/LIPIcs.ICALP.2024.63.
  20. Jugal Garg, Pooja Kulkarni, and Rucha Kulkarni. Approximating Nash social welfare under submodular valuations through (un)matchings. In Proceedings of the 31st Annual ACM-SIAM Symposium on Discrete Algorithms, pages 2673-2687, 2020. URL: https://doi.org/10.1145/3613452.
  21. Ali Ghodsi, Matei Zaharia, Benjamin Hindman, Andy Konwinski, Scott Shenker, and Ion Stoica. Dominant resource fairness: Fair allocation of multiple resource types. In Proceedings of the 8th USENIX Symposium on Networked Systems Design and Implementation, 2011. URL: https://doi.org/10.5555/1972457.1972490.
  22. Vasilis Gkatzelis, Alexandros Psomas, and Xizhi Tan. Fair and efficient online allocations with normalized valuations. In Proceedings of the 35th AAAI Conference on Artificial Intelligence, pages 5440-5447, 2021. URL: https://doi.org/10.1609/aaai.v35i6.16685.
  23. MohammadTaghi Hajiaghayi, Debmalya Panigrahi, Mohammad Khani, and Max Springer. Online algorithms for the Santa Claus problem. In Proceedings of the 36th Annual Conference on Advances in Neural Information Processing Systems, pages 30732-30743, 2022. URL: https://doi.org/10.5555/3600270.3602498.
  24. Zhiyi Huang, Minming Li, Xinkai Shu, and Tianze Wei. Online nash welfare maximization without predictions. In Proceedings of the 19th International Conference on Web and Internet Economics, pages 402-419. Springer, 2023. URL: https://doi.org/10.1007/978-3-031-48974-7_23.
  25. Zhiyi Huang, Zhihao Gavin Tang, and David Wajc. Online matching: A brief survey. ACM SIGecom Exchanges, 22:135-158, 2024. URL: https://doi.org/10.1145/3699824.3699837.
  26. Bala Kalyanasundaram and Kirk R Pruhs. An optimal deterministic algorithm for online b-matching. Theoretical Computer Science, 233(1-2):319-325, 2000. URL: https://doi.org/10.1016/S0304-3975(99)00140-1.
  27. Richard Karp, Umesh Vazirani, and Vijay Vazirani. An optimal algorithm for on-line bipartite matching. In Proceedings of the 22nd Annual ACM Symposium on Theory of Computing, pages 352-358, 1990. URL: https://doi.org/10.1145/100216.100262.
  28. Euiwoong Lee. APX-hardness of maximizing Nash social welfare with indivisible items. Information Processing Letters, 122:17-20, 2017. URL: https://doi.org/10.1016/j.ipl.2017.01.012.
  29. Wenzheng Li and Jan Vondrák. A constant-factor approximation algorithm for nash social welfare with submodular valuations. In Proceedings of the 62nd Annual IEEE Symposium on Foundations of Computer Science, pages 25-36, 2022. URL: https://doi.org/10.1109/FOCS52979.2021.00012.
  30. Aranyak Mehta. Online matching and ad allocation. Foundations and Trends in Theoretical Computer Science, 8(4):265-368, 2013. URL: https://doi.org/10.1561/0400000057.
  31. Hervé Moulin. Fair division and collective welfare. MIT press, 2004. URL: https://doi.org/10.7551/mitpress/2954.001.0001.
  32. Hal R Varian. Equity, envy, and efficiency. Journal of Economic Theory, 9(1):63-91, 1974. URL: https://doi.org/10.1016/0022-0531(74)90075-1.
  33. Toby Walsh. Online cake cutting. In Proceedings of the 2nd International Conference on Algorithmic Decision Theory, pages 292-305. Springer, 2011. URL: https://doi.org/10.1007/978-3-642-24873-3_22.
  34. David Zeng and Alexandros Psomas. Fairness-efficiency tradeoffs in dynamic fair division. In Proceedings of the 21st ACM Conference on Economics and Computation, pages 911-912, 2020. URL: https://doi.org/10.1145/3391403.3399467.
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