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We study the problem of fairly allocating a set of $m$ goods among $n$ agents in the asymptotic setting, where each item's value for each agent is drawn from an underlying joint distribution. Prior works have shown that if this distribution…

Computer Science and Game Theory · Computer Science 2025-12-12 Jugal Garg , Vishnu V. Narayan , Yuang Eric Shen

We study the problem of computing \emph{fair} divisions of a set of indivisible goods among agents with \emph{additive} valuations. For the past many decades, the literature has explored various notions of fairness, that can be primarily…

Computer Science and Game Theory · Computer Science 2025-01-22 Hannaneh Akrami , Nidhi Rathi

We study the problem of fairly allocating $m$ indivisible items arriving online, among $n$ (offline) agents. Although envy-freeness has emerged as the archetypal fairness notion, envy-free (EF) allocations need not exist with indivisible…

Computer Science and Game Theory · Computer Science 2025-10-16 Pooja Kulkarni , Ruta Mehta , Vishnu V. Narayan , Tomasz Ponitka

Several relaxations of envy-freeness, tailored to fair division in settings with indivisible goods, have been introduced within the last decade. Due to the lack of general existence results for most of these concepts, great attention has…

Computer Science and Game Theory · Computer Science 2021-03-09 Georgios Amanatidis , Apostolos Ntokos , Evangelos Markakis

We study the fair allocation of indivisible goods across groups of agents, where each agent fully enjoys all goods allocated to their group. We focus on groups of two (couples) and other groups of small size. For two couples, an EF1…

Computer Science and Game Theory · Computer Science 2025-08-20 Paul Gölz , Hannane Yaghoubizade

We study the problem of fairly allocating indivisible items and a desirable heterogeneous divisible good (i.e., cake) to agents with additive utilities. In our paper, each indivisible item can be a good that yields non-negative utilities to…

Computer Science and Game Theory · Computer Science 2025-11-10 Haris Aziz , Xinhang Lu , Simon Mackenzie , Mashbat Suzuki

We study the allocation of indivisible goods among groups of agents using well-known fairness notions such as envy-freeness and proportionality. While these notions cannot always be satisfied, we provide several bounds on the optimal…

Computer Science and Game Theory · Computer Science 2022-08-24 Pasin Manurangsi , Warut Suksompong

Resource allocation is fundamental to a variety of societal decision-making settings, ranging from the distribution of charitable donations to assigning limited public housing among interested families. A central challenge in this context…

Computer Science and Game Theory · Computer Science 2025-06-11 Hadi Hosseini , Joshua Kavner , Sujoy Sikdar , Rohit Vaish , Lirong Xia

We propose a notion of fairness for allocation problems in which different agents may have different reservation utilities, stemming from different outside options, or property rights. Fairness is usually understood as the absence of envy,…

Theoretical Economics · Economics 2020-05-12 Federico Echenique , Antonio Miralles , Jun Zhang

We investigate the problem of fairly allocating indivisible goods among interested agents using the concept of maximin share. Procaccia and Wang showed that while an allocation that gives every agent at least her maximin share does not…

Computer Science and Game Theory · Computer Science 2018-04-19 Warut Suksompong

We study the problem of fairly and efficiently allocating indivisible goods among agents with additive valuations. We focus on envy-freeness up to any good (EFX) -- an important fairness notion in fair division of indivisible goods. A…

Computer Science and Game Theory · Computer Science 2026-01-08 Vladimir Davidiuk , Yuriy Dementiev , Artur Ignatiev , Danil Sagunov

A collection of objects, some of which are good and some are bad, is to be divided fairly among agents with different tastes, modeled by additive utility functions. If the objects cannot be shared, so that each of them must be entirely…

Computer Science and Game Theory · Computer Science 2022-11-10 Fedor Sandomirskiy , Erel Segal-Halevi

We study the problem of fair and efficient allocation of a set of indivisible chores to agents with additive cost functions. We consider the popular fairness notion of envy-freeness up to one good (EF1) with the efficiency notion of…

Computer Science and Game Theory · Computer Science 2021-10-20 Jugal Garg , Aniket Murhekar , John Qin

We study fair division of indivisible items under a variable input setting, where the set of agents or items may change over time. Starting from an arbitrary allocation, the goal is to restore envy-freeness up to one item (EF1) through item…

Computer Science and Game Theory · Computer Science 2026-04-28 Harish Chandramouleeswaran , Prajakta Nimbhorkar , Nidhi Rathi

Fairness has emerged as an important consideration in algorithmic decision-making. Unfairness occurs when an agent with higher merit obtains a worse outcome than an agent with lower merit. Our central point is that a primary cause of…

Machine Learning · Computer Science 2021-11-11 Ashudeep Singh , David Kempe , Thorsten Joachims

In this work, we revisit the problem of fairly allocating a number of indivisible items that are located on a line to multiple agents. A feasible allocation requires that the allocated items to each agent are connected on the line. The…

Computer Science and Game Theory · Computer Science 2022-05-24 Ankang Sun , Bo Li

We consider the fundamental problem of fairly allocating a set of indivisible items among agents having valuations that are represented by a multi-graph -- here, agents appear as vertices and items as edges between them and each vertex…

Computer Science and Game Theory · Computer Science 2025-10-16 Mahyar Afshinmehr , Alireza Danaei , Mehrafarin Kazemi , Kurt Mehlhorn , Nidhi Rathi

We study the problem of allocating $m$ indivisible items to $n$ agents with additive utilities. It is desirable for the allocation to be both fair and efficient, which we formalize through the notions of envy-freeness and Pareto-optimality.…

Computer Science and Game Theory · Computer Science 2024-05-08 Yushi Bai , Paul Gölz

We study the problem of designing truthful and fair mechanisms when allocating a mixture of divisible and indivisible goods. We first show that there does not exist an EFM (envy-free for mixed goods) and truthful mechanism in general. This…

Computer Science and Game Theory · Computer Science 2023-05-17 Zihao Li , Shengxin Liu , Xinhang Lu , Biaoshuai Tao

The classic house allocation problem is primarily concerned with finding a matching between a set of agents and a set of houses that guarantees some notion of economic efficiency (e.g. utilitarian welfare). While recent works have shifted…

Computer Science and Game Theory · Computer Science 2024-07-08 Hadi Hosseini , Medha Kumar , Sanjukta Roy
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