Skip to main content
SpringerLink
Log in

Online Nash Welfare Maximization Without Predictions

  • Conference paper
  • First Online:
Web and Internet Economics (WINE 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14413))

Included in the following conference series:

  • 499 Accesses

Abstract

The maximization of Nash welfare, which equals the geometric mean of agents’ utilities, is widely studied because it balances efficiency and fairness in resource allocation problems. Banerjee, Gkatzelis, Gorokh, and Jin (2022) recently introduced the model of online Nash welfare maximization for T divisible items and N agents with additive utilities with predictions of each agent’s utility for receiving all items. They gave online algorithms whose competitive ratios are logarithmic. We initiate the study of online Nash welfare maximization without predictions, assuming either that the agents’ utilities for receiving all items differ by a bounded ratio, or that their utilities for the Nash welfare maximizing allocation differ by a bounded ratio. We design online algorithms whose competitive ratios are logarithmic in the aforementioned ratios of agents’ utilities and the number of agents.

This work is supported in part by an NSFC grant (No. 6212290003).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    Banerjee et al. [6] also gave an \(O(\log T)\)-competitive ratio where T is the number of items, under the assumption that items have unit supplies. Since this paper considers arbitrary supplies, the dependence in T is no longer valid.

  2. 2.

    The original theorem by Banerjee et al. [6] only claimed a weaker bound of \(\log ^{1-\varepsilon } N\) but their proof actually showed a slightly stronger bound that we restate here.

References

  1. Alon, N.: Splitting necklaces. Adv. Math. 63(3), 247–253 (1987)

    Article  MathSciNet  Google Scholar 

  2. Alon, N., Awerbuch, B., Azar, Y., Buchbinder, N., Naor, J.: A general approach to online network optimization problems. ACM Trans. Algorithms 2(4), 640–660 (2006)

    Article  MathSciNet  Google Scholar 

  3. Anari, N., Mai, T., Gharan, S.O., Vazirani, V.V.: Nash social welfare for indivisible items under separable, piecewise-linear concave utilities. In: Proceedings of the 29th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 2274–2290 (2018)

    Google Scholar 

  4. Anari, N., Gharan, S.O., Saberi, A., Singh, M.: Nash social welfare, matrix permanent, and stable polynomials. In: Proceedings of the 8th Innovations in Theoretical Computer Science Conference, p. 36 (2017)

    Google Scholar 

  5. Azar, Y., Buchbinder, N., Jain, K.: How to allocate goods in an online market? In: de Berg, M., Meyer, U. (eds.) ESA 2010. LNCS, vol. 6347, pp. 51–62. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15781-3_5

    Chapter  Google Scholar 

  6. Banerjee, S., Gkatzelis, V., Gorokh, A., Jin, B.: Online Nash social welfare maximization with predictions. In: Proceedings of the 33rd Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1–19 (2022)

    Google Scholar 

  7. Banerjee, S., Gkatzelis, V., Hossain, S., Jin, B., Micha, E., Shah, N.: Proportionally fair online allocation of public goods with predictions. arXiv preprint arXiv:2209.15305 (2022)

  8. Barman, S., Bhaskar, U., Krishna, A., Sundaram, R.G.: Tight approximation algorithms for p-mean welfare under subadditive valuations. In: Proceedings of the 28th Annual European Symposium on Algorithms, pp. 11:1–11:17 (2020)

    Google Scholar 

  9. Barman, S., Khan, A., Maiti, A.: Universal and tight online algorithms for generalized-mean welfare. In: Proceedings of the AAAI Conference on Artificial Intelligence, pp. 4793–4800 (2022)

    Google Scholar 

  10. Barman, S., Krishnamurthy, S.K., Vaish, R.: Finding fair and efficient allocations. In: Proceedings of the 19th ACM Conference on Economics and Computation, pp. 557–574 (2018)

    Google Scholar 

  11. Buchbinder, N., Naor, J.: Online primal-dual algorithms for covering and packing. Math. Oper. Res. 34(2), 270–286 (2009)

    Article  MathSciNet  Google Scholar 

  12. Chaudhury, B.R., Garg, J., Mehta, R.: Fair and efficient allocations under subadditive valuations. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 35, pp. 5269–5276 (2021)

    Google Scholar 

  13. Cole, R., et al.: Convex program duality, Fisher markets, and Nash social welfare. In: Proceedings of the 18th ACM Conference on Economics and Computation, pp. 459–460 (2017)

    Google Scholar 

  14. Cole, R., Gkatzelis, V.: Approximating the Nash social welfare with indivisible items. In: Proceedings of the 47th Annual ACM Symposium on Theory of Computing, pp. 371–380 (2015)

    Google Scholar 

  15. Devanur, N.R., Jain, K.: Online matching with concave returns. In: Proceedings of the 44th Annual ACM Symposium on Theory of Computing, pp. 137–144 (2012)

    Google Scholar 

  16. Dubins, L.E., Spanier, E.H.: How to cut a cake fairly. Am. Math. Monthly 68(1P1), 1–17 (1961)

    Google Scholar 

  17. Eisenberg, E., Gale, D.: Consensus of subjective probabilities: the pari-mutuel method. Ann. Math. Stat. 30(1), 165–168 (1959)

    Article  MathSciNet  Google Scholar 

  18. Gao, Y., Peysakhovich, A., Kroer, C.: Online market equilibrium with application to fair division. In: Advances in Neural Information Processing Systems, vol. 34, pp. 27305–27318 (2021)

    Google Scholar 

  19. Garg, J., Hoefer, M., Mehlhorn, K.: Approximating the Nash social welfare with budget-additive valuations. In: Proceedings of the 29th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 2326–2340 (2018)

    Google Scholar 

  20. Garg, J., Kulkarni, P., Kulkarni, R.: Approximating Nash social welfare under submodular valuations through (un)matchings. In: Proceedings of the 31st Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 2673–2687 (2020)

    Google Scholar 

  21. Gkatzelis, V., Psomas, A., Tan, X.: Fair and efficient online allocations with normalized valuations. In: Proceedings of the AAAI Conference on Artificial Intelligence, pp. 5440–5447 (2021)

    Google Scholar 

  22. Hao, F., Kodialam, M., Lakshman, T., Mukherjee, S.: Online allocation of virtual machines in a distributed cloud. IEEE/ACM Trans. Networking 25(1), 238–249 (2016)

    Article  Google Scholar 

  23. Hardy, G.H., Littlewood, J.E., Pólya, G.: Inequalities. Cambridge University Press, Cambridge (1952)

    Google Scholar 

  24. Kaneko, M., Nakamura, K.: The Nash social welfare function. Econometrica 47(2), 423–435 (1979)

    Article  MathSciNet  Google Scholar 

  25. Karp, R.M., Vazirani, U.V., Vazirani, V.V.: An optimal algorithm for on-line bipartite matching. In: Proceedings of the 22nd Annual ACM Symposium on Theory of Computing, pp. 352–358 (1990)

    Google Scholar 

  26. Lee, E.: APX-hardness of maximizing Nash social welfare with indivisible items. Inf. Process. Lett. 122, 17–20 (2017)

    Article  MathSciNet  Google Scholar 

  27. Li, W., Vondrák, J.: A constant-factor approximation algorithm for Nash social welfare with submodular valuations. In: 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science, pp. 25–36 (2022)

    Google Scholar 

  28. Liao, L., Gao, Y., Kroer, C.: Nonstationary dual averaging and online fair allocation. In: Advances in Neural Information Processing Systems, vol. 35, pp. 37159–37172 (2022)

    Google Scholar 

  29. Mehta, A.: Online matching and ad allocation. Found. Trends Theor. Comput. Sci. 8(4), 265–368 (2013)

    Article  MathSciNet  Google Scholar 

  30. Moulin, H.: Fair Division and Collective Welfare. MIT Press, Cambridge (2004)

    Google Scholar 

  31. Nash, J.F., Jr.: The bargaining problem. Econometrica 18(2), 155–162 (1950)

    Article  MathSciNet  Google Scholar 

  32. Prendergast, C.: How food banks use markets to feed the poor. J. Econ. Perspect. 31(4), 145–162 (2017)

    Article  Google Scholar 

  33. Varian, H.R.: Equity, envy, and efficiency. J. Econ. Theory 9(1), 63–91 (1974)

    Article  MathSciNet  Google Scholar 

  34. Vazirani, V.V.: Combinatorial algorithms for market equilibria. In: Algorithmic Game Theory, pp. 103–134. Cambridge University Press (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Hong Kong, Kowloon, Hong Kong

    Zhiyi Huang & Xinkai Shu

  2. City University of Hong Kong, Kowloon, Hong Kong

    Minming Li & Tianze Wei

Authors
  1. Zhiyi Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Minming Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xinkai Shu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Tianze Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhiyi Huang .

Editor information

Editors and Affiliations

  1. Department of Industrial and Enterprise Systems Engineering, University of Illinois System, Urbana, IL, USA

    Jugal Garg

  2. Institute of Mathematics, Technische Universität Berlin, Berlin, Berlin, Germany

    Max Klimm

  3. Center on Frontiers of Computing Studies, Peking University, Beijing, Beijing, China

    Yuqing Kong

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Huang, Z., Li, M., Shu, X., Wei, T. (2024). Online Nash Welfare Maximization Without Predictions. 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_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-48974-7_23

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-48973-0

  • Online ISBN: 978-3-031-48974-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation