Top

Published in:

2022 | OriginalPaper | Chapter

Envy Freeness Up to One Item: Shall We Duplicate or Remove Resources?

Author : Martin Aleksandrov

Published in: Progress in Artificial Intelligence

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

We consider a fair division model in which agents have general valuations for bundles of indivisible items. We propose two new approximate properties for envy freeness of allocations in this model: DEFX and DEF1. We compare these with two existing axiomatic properties: EFX and EF1. For example, we give the first result confirming that EFX allocations may not exist with general but identical valuations. However, even when they do exist in such problems, we prove that DEFX (and, therefore DEF1) and PO allocations exist whereas EFX and PO allocations may not exist. Our results assert eloquently that DEFX and DEF1 approximate fairness better than EFX and EF1.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Skill Learning for Long-Horizon Sequential Tasks

next chapter Learning to Cooperate with Completely Unknown Teammates

Aleksandrov, M., Aziz, H., Gaspers, S., Walsh, T.: Online fair division: analysing a food bank problem. In: Proceedings of IJCAI 2015, Buenos Aires, Argentina, 25–31 July 2015, pp. 2540–2546 (2015). http://ijcai.org/papers15/Abstracts/IJCAI15-360.html

Aleksandrov, M., Walsh, T.: Two algorithms for additive and fair division of mixed manna. In: KI 2020: Advances in Artificial Intelligence - 43th Annual German Conference on AI, Bamberg, Germany, 21–25 September 2020, Proceedings, pp. 44–57 (2020). https://doi.org/10.1007/978-3-030-58285-2_1

Aziz, H., Caragiannis, I., Igarashi, A., Walsh, T.: Fair allocation of indivisible goods and chores. In: Proceedings of the 28th International Joint Conference on Artificial Intelligence, pp. 53–59. IJCAI 2019, AAAI Press (2019). https://dl.acm.org/doi/abs/10.5555/3367032.3367041

Budish, E.: The combinatorial assignment problem: approximate competitive equilibrium from equal incomes. J. Polit. Econ. 119(6), 1061–1103 (2011). https://doi.org/10.1086/664613CrossRef

Budish, E., Cantillon, E.: The multi-unit assignment problem: theory and evidence from course allocation at Harvard. Am. Econ. Rev. 102(5), 2237–2271 (2012). https://doi.org/10.1257/aer.102.5.2237CrossRef

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). https://doi.org/10.1145/3355902MathSciNetCrossRef

Chen, X., Liu, Z.: The fairness of leximin in allocation of indivisible chores. CoRR abs/2005.04864 (2020). https://arxiv.org/abs/2005.04864

Dubins, L.E., Spanier, E.H.: How to cut a cake fairly. Am. Math. Mon. 68(1), 1–17 (1961). https://doi.org/10.2307/2311357MathSciNetCrossRefMATH

Foley, D.K.: Resource allocation and the public sector. Yale Econ. Essays 7(1), 45–98 (1967). https://www.proquest.com/openview/cac1d2d0d079f04d1989726c2c2181fa/1?pq-origsite=gscholar &cbl=18750 &diss=y

10.

Lipton, R.J., Markakis, E., Mossel, E., Saberi, A.: On approximately fair allocations of indivisible goods. In: Proceedings Fifth ACM Conference on Electronic Commerce (EC-2004), New York, NY, USA, 17–20 May 2004, pp. 125–131 (2004). https://doi.org/10.1145/988772.988792

11.

Pareto, V.: Cours d’économie politique. Œuvres complètes publiées sous la direction de giovanni busino. tomes 1 et 2 en un volume (1897). https://doi.org/10.3917/droz.paret.1964.01. 9782600040143

12.

Plaut, B., Roughgarden, T.: Almost envy-freeness with general valuations. In: Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018, New Orleans, LA, USA, 7–10 January 2018, pp. 2584–2603 (2018). https://doi.org/10.1137/19M124397X

13.

Tan, M., Dai, Z., Ren, Y., Walsh, T., Aleksandrov, M.: Minimal-envy conference paper assignment: formulation and a fast iterative algorithm. In: 2021 5th Asian Conference on Artificial Intelligence Technology (ACAIT), pp. 667–674 (2021). https://doi.org/10.1109/ACAIT53529.2021.9731163

Title: Envy Freeness Up to One Item: Shall We Duplicate or Remove Resources?
Author: Martin Aleksandrov
Publisher: Springer International Publishing
Book: Progress in Artificial Intelligence
Print ISBN: 978-3-031-16473-6

Electronic ISBN: 978-3-031-16474-3

Copyright Year: 2022
DOI: https://doi.org/10.1007/978-3-031-16474-3_59

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Premium Partner