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EFX Under Budget Constraint

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Frontiers of Algorithmic Wisdom (IJTCS-FAW 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13461))

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Abstract

Fair division captures many real-world scenarios and plays an important role in many research fields including computer science, economy, operations research, etc. For the problem of indivisible goods allocation, it is well-known that an allocation satisfying the maximum Nash Social Welfare (Max-NSW) is envy-free up to one good (EF1), which is an important fairness concept. However, EF1 is often considered to be somewhat weak since one may remove the most valuable good. In this paper, we investigate the relationship between the Max-NSW allocation and a stronger fairness concept, envy-free up to any good (EFX), which means the envyness disappears after the removal of the least valuable good. We focus on the budget-feasible variant in which each agent has a budget to cover the total cost of goods she gets. We show that a Max-NSW allocation guarantees \(\frac{1}{4}\)-EFX when agents’ value are in the Binary \(\{0,1\}\) . Moreover, we provide an algorithm to find a budget-feasible EFX allocation for the Binary variant.

Supported by the National Key Research and Development Project of China (Grant No. 2019YFB2102500), NSFC (Grant No. 12071460, 62102117), the Fundamental Research Project of Shenzhen City (No. JCYJ20210324102012033) and the Shenzhen Science and Technology Program (Grant No. RCBS20210609103900003).

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References

  1. Amanatidis, G., Birmpas, G., Filos-Ratsikas, A., Hollender, A., Voudouris, A.A.: Maximum Nash welfare and other stories about EFX. In: Proceedings of the 29th International Joint Conference on Artificial Intelligence, pp. 24–30. IJCAI 2020, AAAI Press, Yokohama, Japan (2020)

    Google Scholar 

  2. 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. EC 2018, ACM, New York, NY, USA (2018)

    Google Scholar 

  3. Barman, S., Krishnamurthy, S.K., Vaish, R.: Greedy algorithms for maximizing Nash social welfare. In: Proceedings of the 17th International Conference on Autonomous Agents and MultiAgent Systems, pp. 7–13. AAMAS 2018, ACM, Stockholm, Sweden (2018)

    Google Scholar 

  4. Biswas, A., Barman, S.: Fair division under cardinality constraints. In: Proceedings of the 27th International Joint Conference on Artificial Intelligence, pp. 91–97. IJCAI 2018, AAAI Press, Stockholm, Sweden (2018)

    Google Scholar 

  5. Caragiannis, I., Gravin, N., Huang, X.: Envy-freeness up to any item with high Nash welfare: The virtue of donating items. In: Proceedings of the 20th ACM Conference on Economics and Computation, pp. 527–545. EC 2019, ACM, New York, NY, USA (2019)

    Google Scholar 

  6. Caragiannis, I., Kurokawa, D., Moulin, H., Procaccia, A.D., Shah, N., Wang, J.: The unreasonable fairness of maximum Nash welfare. ACM Trans. Econ. Comput. 7(3), 1–32 (2019)

    Article  MathSciNet  Google Scholar 

  7. Chaudhury, B.R., Garg, J., Mehlhorn, K.: EFX exists for three agents. In: Proceedings of the 21st ACM Conference on Economics and Computation, pp. 1–19. EC 2020, ACM, New York, NY, USA (2020)

    Google Scholar 

  8. Chaudhury, B.R., Kavitha, T., Mehlhorn, K., Sgouritsa, A.: A little charity guarantees almost envy-freeness. SIAM J. Comput. 50(4), 1336–1358 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  9. Cole, R., Devanur, N., Gkatzelis, V., Jain, K., Mai, T., Vazirani, V.V., Yazdanbod, S.: Convex program duality, fisher markets, and Nash social welfare. In: Proceedings of the 18th ACM Conference on Economics and Computation, pp. 459–460. EC 2017, ACM, New York, NY, USA (2017)

    Google Scholar 

  10. Cole, R., Gkatzelis, V.: Approximating the Nash social welfare with indivisible items. In: Proceedings of the Forty-Seventh Annual ACM Symposium on Theory of Computing, pp. 371–380. STOC 2015, ACM, New York, NY, USA (2015)

    Google Scholar 

  11. Dolev, D., Feitelson, D.G., Halpern, J.Y., Kupferman, R., Linial, N.: No justified complaints: on fair sharing of multiple resources. In: Innovations in Theoretical Computer Science, pp. 68–75. ITCS 2012, ACM, New York, NY, USA (2012)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  13. Gan, J., Li, B., Wu, X.: Approximately envy-free budget-feasible allocation (2021). https://arxiv.org/abs/2106.14446

  14. Garg, J., Kulkarni, P., Kulkarni, R.: Approximating Nash social welfare under submodular valuations through (un)matchings. In: Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms, pp. 2673–2687. SOSA 2020, SIAM, Salt Lake City, UT, USA (2020)

    Google Scholar 

  15. Ghodsi, A., Zaharia, M., Hindman, B., Konwinski, A., Shenker, S., Stoica, I.: Dominant resource fairness: Fair allocation of multiple resource types. In: Proceedings of the 8th USENIX Conference on Networked Systems Design and Implementation, pp. 323–336. NSDI 2011, USENIX Association, USA (2011)

    Google Scholar 

  16. Grandl, R., Ananthanarayanan, G., Kandula, S., Rao, S., Akella, A.: Multi-resource packing for cluster schedulers. In: ACM SIGCOMM 2014 Conference, pp. 455–466. SIGCOMM 2014, ACM, Chicago, IL, USA (2014)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  19. Li, P., Hua, Q., Hu, Z., Ting, H.-F., Zhang, Y.: Approximation algorithms for the selling with preference. J. Combinat. Optim. 40(2), 366–378 (2020). https://doi.org/10.1007/s10878-020-00602-3

    Article  MathSciNet  MATH  Google Scholar 

  20. Lipton, R., Markakis, E., Mossel, E., Saberi, A.: On approximately fair allocations of indivisible goods. In: Proceedings of the 5th ACM Conference on Electronic Commerce, pp. 125–131. EC 2004, ACM, New York, NY, USA (2004)

    Google Scholar 

  21. Moulin, H.: Fair Division and Collective Welfare, vol. 1, 1st edn. MIT Press (2003)

    Google Scholar 

  22. Wu, X., Li, B., Gan, J.: Budget-feasible maximum Nash social welfare allocation is almost envy-free (2020). https://arxiv.org/abs/2012.03766

  23. Zhang, Y., Chin, F.Y., Poon, S.H., Ting, H.F., Xu, D., Yu, D.: Offline and online algorithms for single-minded selling problem. Theoret. Comput. Sci. 821, 15–22 (2020)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, People’s Republic of China

    Sijia Dai, Guichen Gao, Li Ning, Yicheng Xu & Yong Zhang

  2. Harbin Institute of Technology (Shenzhen), Shenzhen, People’s Republic of China

    Shengxin Liu

  3. Tunku Abdul Rahman University, Kajang, Malaysia

    Boon Han Lim

Authors
  1. Sijia Dai
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  2. Guichen Gao
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  3. Shengxin Liu
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  4. Boon Han Lim
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  5. Li Ning
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  6. Yicheng Xu
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  7. Yong Zhang
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Correspondence to Yong Zhang .

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Editors and Affiliations

  1. Department of Computer Science, City University of Hong Kong, Hong Kong, China

    Minming Li

  2. Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China

    Xiaoming Sun

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Dai, S. et al. (2022). EFX Under Budget Constraint. In: Li, M., Sun, X. (eds) Frontiers of Algorithmic Wisdom. IJTCS-FAW 2022. Lecture Notes in Computer Science, vol 13461. Springer, Cham. https://doi.org/10.1007/978-3-031-20796-9_1

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  • DOI: https://doi.org/10.1007/978-3-031-20796-9_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-20795-2

  • Online ISBN: 978-3-031-20796-9

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