Maximum Nash welfare and other stories about EFX

Amanatidis, Georgios; Birmpas, Georgios; Filos-Ratsikas, Aris; Hollender, Alexandros; Voudouris, Alexandros A.

doi:10.1016/j.tcs.2021.02.020

Cited by 31 publications

(27 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Before discussing the proof of Theorem 1, let us compare it with some known results on the hardness of maximizing Nash welfare in the fair division literature. Amanatidis et al (2021) have shown that maximizing Nash welfare is NP-hard for 3-value instances when all valuations are in the range {0, 1, a} for some a > 1. The parameter 'a' in their construction depends on the size of the instance; specifically, they use a > 1/ 2m √ 2 − 1, where m is the number of clauses in the 3-SAT instance which they reduce from.…”

Section: Hardness Resultsmentioning

confidence: 99%

“…It strikes a balance between the oftenconflicting goals of fairness and economic efficiency, and enjoys a strong axiomatic support (Moulin 2004;Caragiannis et al 2019). In recent years, the computational aspects of Nash welfare have gained considerable attention (Cole and Gkatzelis 2018;Barman, Krishnamurthy, and Vaish 2018a;Amanatidis et al 2021;Akrami et al 2022).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Maximizing Nash Social Welfare under Two-Sided Preferences

Jain,

Vaish

2024

AAAI

View full text Add to dashboard Cite

The maximum Nash social welfare (NSW)---which maximizes the geometric mean of agents' utilities---is a fundamental solution concept with remarkable fairness and efficiency guarantees. The computational aspects of NSW have been extensively studied for *one-sided* preferences where a set of agents have preferences over a set of resources. Our work deviates from this trend and studies NSW maximization for *two-sided* preferences, wherein a set of workers and firms, each having a cardinal valuation function, are matched with each other. We provide a systematic study of the computational complexity of maximizing NSW for many-to-one matchings under two-sided preferences. Our main negative result is that maximizing NSW is NP-hard even in a highly restricted setting where each firm has capacity 2, all valuations are in the range {0,1,2}, and each agent positively values at most three other agents. In search of positive results, we develop approximation algorithms as well as parameterized algorithms in terms of natural parameters such as the number of workers, the number of firms, and the firms' capacities. We also provide algorithms for restricted domains such as symmetric binary valuations and bounded degree instances.

show abstract

Section: Hardness Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Maximizing Nash Social Welfare under Two-Sided Preferences

Jain,

Vaish

2024

AAAI

View full text Add to dashboard Cite

show abstract

“…Furthermore, our efforts to ensure a 1WEF allocation highlight that the standard round-robin procedure requires specific adjustments to encompass the asymmetric agent configuration. Consequently, the amalgamation of these two approaches, though effective in yielding a (' 1)-EFX allocation (Amanatidis et al 2021), does not naturally expand to address this extended problem.…”

Section: Discussionmentioning

confidence: 99%

Almost Envy-Free Allocations of Indivisible Goods or Chores with Entitlements

Springer,

Hajiaghayi,

Yami

2024

AAAI

View full text Add to dashboard Cite

We here address the problem of fairly allocating indivisible goods or chores to n agents with weights that define their entitlement to the set of indivisible resources. Stemming from well-studied fairness concepts such as envy-freeness up to one good (EF1) and envy-freeness up to any good (EFX) for agents with equal entitlements, we present, in this study, the first set of impossibility results alongside algorithmic guarantees for fairness among agents with unequal entitlements. Within this paper, we expand the concept of envy-freeness up to any good or chore to the weighted context (WEFX and XWEF respectively), demonstrating that these allocations are not guaranteed to exist for two or three agents. Despite these negative results, we develop a WEFX procedure for two agents with integer weights, and furthermore, we devise an approximate WEFX procedure for two agents with normalized weights. We further present a polynomial-time algorithm that guarantees a weighted envy-free allocation up to one chore (1WEF) for any number of agents with additive cost functions. Our work underscores the heightened complexity of the weighted fair division problem when compared to its unweighted counterpart.

show abstract

“…Moreover, our algorithm serves as the foundation for our second positive result, which is an efficient procedure deciding the existence of an EFX/EF1/EF allocation for the combined parameter the number of agents and the number of different values in agents' preferences. The latter parameter naturally captures widely studied binary valuations (Barman, Krishnamurthy, and Vaish 2018;Freeman et al 2019;Halpern et al 2020;Babaioff, Ezra, and Feige 2021;Suksompong and Teh 2022), bi-valued valuations (Ebadian, Peters, and Shah 2022;Garg, Murhekar, and Qin 2022), and was previously used by Amanatidis et al (2021) and Garg and Murhekar (2023).…”

Section: Our Contributionmentioning

confidence: 99%

The Complexity of Fair Division of Indivisible Items with Externalities

Deligkas,

Eiben,

Korchemna

et al. 2024

AAAI

View full text Add to dashboard Cite

We study the computational complexity of fairly allocating a set of indivisible items under externalities. In this recently-proposed setting, in addition to the utility the agent gets from their bundle, they also receive utility from items allocated to other agents. We focus on the extended definitions of envy-freeness up to one item (EF1) and of envy-freeness up to any item (EFX), and we provide the landscape of their complexity for several different scenarios. We prove that it is NP-complete to decide whether there exists an EFX allocation, even when there are only three agents, or even when there are only six different values for the items. We complement these negative results by showing that when both the number of agents and the number of different values for items are bounded by a parameter the problem becomes fixed-parameter tractable. Furthermore, we prove that two-valued and binary-valued instances are equivalent and that EFX and EF1 allocations coincide for this class of instances. Finally, motivated from real-life scenarios, we focus on a class of structured valuation functions, which we term agent/item-correlated. We prove their equivalence to the "standard" setting without externalities. Therefore, all previous results for EF1 and EFX apply immediately for these valuations.

show abstract

Maximum Nash welfare and other stories about EFX

Cited by 31 publications

References 24 publications

Maximizing Nash Social Welfare under Two-Sided Preferences

Maximizing Nash Social Welfare under Two-Sided Preferences

Almost Envy-Free Allocations of Indivisible Goods or Chores with Entitlements

The Complexity of Fair Division of Indivisible Items with Externalities

Contact Info

Product

Resources

About