# Fair and Efficient Allocations under Subadditive Valuations

@inproceedings{Chaudhury2021FairAE, title={Fair and Efficient Allocations under Subadditive Valuations}, author={Bhaskar Ray Chaudhury and Jugal Garg and Ruta Mehta}, booktitle={AAAI}, year={2021} }

We study the problem of allocating a set of indivisible goods among agents with subadditive valuations in a fair and efficient manner. Envy-Freeness up to any good (EFX) is the most compelling notion of fairness in the context of indivisible goods. Although the existence of EFX is not known beyond the simple case of two agents with subadditive valuations, some good approximations of EFX are known to exist, namely $\tfrac{1}{2}$-EFX allocation and EFX allocations with bounded charity.
Nash…

## 18 Citations

Fair and Efficient Allocations under Lexicographic Preferences

- EconomicsAAAI
- 2021

This work proves the existence of EFX and Pareto optimal allocations, and provides an algorithmic characterization of these two properties, and characterize the mechanisms that are, in addition, strategyproof, non-bossy, and neutral.

On Approximate Envy-Freeness for Indivisible Chores and Mixed Resources

- EconomicsAPPROX-RANDOM
- 2021

It is shown that determining the existence of an envy-free allocation is NP-complete even when agents have binary additive valuations, and a polynomial-time algorithm is provided for computing an allocation that satisfies envy-freeness up to one chore (EF1) under monotone valuations.

Almost Envy-freeness, Envy-rank, and Nash Social Welfare Matchings

- EconomicsAAAI
- 2021

This paper proposes another fairness criterion, namely envy-freeness up to a random good or EFR, which is weaker than EFX, yet stronger than EF1, and provides a polynomial-time $0.73$-approximation allocation algorithm which makes a connection between Nash Social Welfare and envy freeness.

Approximating Nash social welfare under rado valuations

- Computer ScienceSTOC
- 2021

The approach gives the first constant-factor approximation algorithm for the asymmetric case under Rado valuations, provided that the maximum ratio between the weights is bounded by a constant.

Tight Approximation Algorithms for p-Mean Welfare Under Subadditive Valuations

- Computer ScienceESA
- 2020

Polynomial-time algorithms for the fair and efficient allocation of indivisible goods among agents that have subadditive valuations over the goods and approximation guarantees are essentially tight for XOS and, hence, subadditives valuations are developed.

Approximating Maximin Shares with Mixed Manna

- Computer ScienceArXiv
- 2020

The study of fair allocations of a mixed manna under the popular fairness notion of maximin share is initiated, and a PTAS - an efficient algorithm to find a MMS allocation given $\alpha-\epsilon>0$ for the best possible $\alpha$ is designed.

Improved Maximin Guarantees for Subadditive and Fractionally Subadditive Fair Allocation Problem

- Computer Science, MathematicsProceedings of the AAAI Conference on Artificial Intelligence
- 2022

It is proved that when the valuation functions are fractionally subadditive, a 1/4.6-MMS allocation is guaranteed to exist and this also improves upon the previous bound of 1/5-M MS guarantee for the fractionallySubadditive setting.

Fair and Efficient Allocations Without Obvious Manipulations

- EconomicsArXiv
- 2022

We consider the fundamental problem of allocating a set of indivisible goods among strategic agents with additive valuation functions. It is well known that, in the absence of monetary transfers,…

Fair and Efficient Division of Indivisibles

- Economics
- 2022

Finding fair allocations is a fundamental problem in algorithmic game theory. With divisible resources, it is commonly phrased as the cake cutting problem and has been extensively studied; see [71]…

Fair Division of Indivisible Goods for a Class of Concave Valuations

- Economics, Computer ScienceJ. Artif. Intell. Res.
- 2022

A polynomial-time algorithm is presented that approximates the optimal Nash social welfare (NSW) up to a factor of e1/e ≈ 1.445, and the upper bounds on the optimal NSW introduced in Cole and Gkatzelis (2018) and Barman et al. ( 2018) have the same value.

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