DeepAI

# Fair and Efficient Allocations under Subadditive Valuations

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 12-EFX allocation and EFX allocations with bounded charity. Nash welfare (the geometric mean of agents' valuations) is one of the most commonly used measures of efficiency. In case of additive valuations, an allocation that maximizes Nash welfare also satisfies fairness properties like Envy-Free up to one good (EF1). Although there is substantial work on approximating Nash welfare when agents have additive valuations, very little is known when agents have subadditive valuations. In this paper, we design a polynomial-time algorithm that outputs an allocation that satisfies either of the two approximations of EFX as well as achieves an 𝒪(n) approximation to the Nash welfare. Our result also improves the current best-known approximation of 𝒪(n log n) and 𝒪(m) to Nash welfare when agents have submodular and subadditive valuations, respectively. Furthermore, our technique also gives an 𝒪(n) approximation to a family of welfare measures, p-mean of valuations for p∈ (-∞, 1], thereby also matching asymptotically the current best known approximation ratio for special cases like p =-∞ while also retaining the fairness properties.

• 16 publications
• 23 publications
• 24 publications
05/15/2020

### Tight Approximation Algorithms for p-Mean Welfare Under Subadditive Valuations

We develop polynomial-time algorithms for the fair and efficient allocat...
02/25/2020

### Fair and Truthful Mechanisms for Dichotomous Valuations

We consider the problem of allocating a set on indivisible items to play...
09/13/2017

### Computing the Shapley Value in Allocation Problems: Approximations and Bounds, with an Application to the Italian VQR Research Assessment Program

In allocation problems, a given set of goods are assigned to agents in s...
12/28/2019

### Approximating Nash Social Welfare under Submodular Valuations through (Un)Matchings

We study the problem of approximating maximum Nash social welfare (NSW) ...
08/15/2022

### A General Framework for Fair Allocation with Matroid Rank Valuations

We study the problem of fairly allocating a set of indivisible goods amo...
07/21/2021

### On Fair and Efficient Allocations of Indivisible Public Goods

We study fair allocation of indivisible public goods subject to cardinal...
03/02/2021

### Improving EFX Guarantees through Rainbow Cycle Number

We study the problem of fairly allocating a set of indivisible goods amo...