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We study the problem of allocating a group of indivisible chores among agents while each chore has a binary marginal. We focus on the fairness criteria of envy-freeness up to any item (EFX) and investigate the existence of EFX allocations.…

Computer Science and Game Theory · Computer Science 2023-08-24 Biaoshuai Tao , Xiaowei Wu , Ziqi Yu , Shengwei Zhou

The classic fair division problems assume the resources to be allocated are either divisible or indivisible, or contain a mixture of both, but the agents always have a predetermined and uncontroversial agreement on the (in)divisibility of…

Computer Science and Game Theory · Computer Science 2025-03-31 Xiaohui Bei , Shengxin Liu , Xinhang Lu

In this paper, we study the classic problem of fairly allocating indivisible items with the extra feature that the items lie on a line. Our goal is to find a fair allocation that is contiguous, meaning that the bundle of each agent forms a…

Computer Science and Game Theory · Computer Science 2019-04-30 Warut Suksompong

Our work studies the fair allocation of indivisible items to a set of agents, and falls within the scope of establishing improved approximation guarantees. It is well known by now that the classic solution concepts in fair division, such as…

Computer Science and Game Theory · Computer Science 2023-08-10 Evangelos Markakis , Christodoulos Santorinaios

We study the fair allocation problem of indivisible items with subsidy. In this paper, we focus on the notion of fairness - equitability (EQ), which requires that items be allocated such that all agents value the bundle they receive…

Computer Science and Game Theory · Computer Science 2025-09-10 Yuanyuan Wang , Tianze Wei

We study the fair division of a collection of $m$ indivisible goods amongst a set of $n$ agents. Whilst envy-free allocations typically do not exist in the indivisible goods setting, envy-freeness can be achieved if some amount of a…

Computer Science and Game Theory · Computer Science 2019-12-06 Johannes Brustle , Jack Dippel , Vishnu V. Narayan , Mashbat Suzuki , Adrian Vetta

We study several fairness notions in allocating indivisible chores (i.e., items with non-positive values) to agents who have additive and submodular cost functions. The fairness criteria we are concern with are envy-free up to any item…

Computer Science and Game Theory · Computer Science 2021-09-29 Ankang Sun , Bo Chen , Xuan Vinh Doan

We study the problem of fairly allocating indivisible goods among agents which are equipped with {\em leveled} valuation functions. Such preferences, that have been studied before in economics and fair division literature, capture a simple…

Computer Science and Game Theory · Computer Science 2025-02-17 George Christodoulou , Vasilis Christoforidis

We study the problem of allocating indivisible items to agents with additive valuations, under the additional constraint that bundles must be connected in an underlying item graph. Previous work has considered the existence and complexity…

Computer Science and Game Theory · Computer Science 2018-11-13 Ayumi Igarashi , Dominik Peters

When dividing items among agents, two of the most widely studied fairness notions are envy-freeness and proportionality. We consider a setting where $m$ chores are allocated to $n$ agents and the disutility of each chore for each agent is…

Computer Science and Game Theory · Computer Science 2025-04-30 Pasin Manurangsi , Warut Suksompong

We study fair allocation of indivisible goods among additive agents with feasibility constraints. In these settings, every agent is restricted to get a bundle among a specified set of feasible bundles. Such scenarios have been of great…

Computer Science and Game Theory · Computer Science 2022-04-26 Amitay Dror , Michal Feldman , Erel Segal-Halevi

We study the fair division problem on divisible heterogeneous resources (the cake cutting problem) with strategic agents, where each agent can manipulate his/her private valuation in order to receive a better allocation. A…

Computer Science and Game Theory · Computer Science 2023-03-31 Xiaolin Bu , Jiaxin Song , Biaoshuai Tao

We study the problem of distributing a set of indivisible items among agents with additive valuations in a $\mathit{fair}$ manner. The fairness notion under consideration is Envy-freeness up to any item (EFX). Despite significant efforts by…

Computer Science and Game Theory · Computer Science 2020-06-02 Bhaskar Ray Chaudhury , Jugal Garg , Kurt Mehlhorn

We consider the discrete assignment problem in which agents express ordinal preferences over objects and these objects are allocated to the agents in a fair manner. We use the stochastic dominance relation between fractional or randomized…

Computer Science and Game Theory · Computer Science 2015-06-18 Haris Aziz , Serge Gaspers , Simon Mackenzie , Toby Walsh

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

Several fairness concepts have been proposed recently in attempts to approximate envy-freeness in settings with indivisible goods. Among them, the concept of envy-freeness up to any item (EFX) is arguably the closest to envy-freeness.…

Computer Science and Game Theory · Computer Science 2019-02-13 Ioannis Caragiannis , Nick Gravin , Xin Huang

We study fair division of indivisible goods in a single-parameter environment. In particular, we develop truthful social welfare maximizing mechanisms for fairly allocating indivisible goods. Our fairness guarantees are in terms of solution…

Computer Science and Game Theory · Computer Science 2019-01-29 Siddharth Barman , Ganesh Ghalme , Shweta Jain , Pooja Kulkarni , Shivika Narang

Fair division mechanisms for indivisible goods require agent orderings to deterministically select one allocation when running the algorithm in practice. We introduce position envy-freeness up to one good (PEF1) as a fairness criterion for…

Computer Science and Game Theory · Computer Science 2025-11-18 Ryoga Mahara , Ryuhei Mizutani , Taihei Oki , Tomohiko Yokoyama

Equitability is a well-studied fairness notion in fair division, where an allocation is equitable if all agents receive equal utility from their allocation. For indivisible items, an exactly equitable allocation may not exist, and a natural…

Computer Science and Game Theory · Computer Science 2025-05-12 Umang Bhaskar , Vishwa Prakash HV , Aditi Sethia , Rakshitha

Although approximate notions of envy-freeness-such as envy-freeness up to one good (EF1)-have been extensively studied for indivisible goods, the seemingly simpler fairness concept of proportionality up to one good (PROP1) has received far…

Computer Science and Game Theory · Computer Science 2025-08-19 Martin Jupakkal Andersen , Ioannis Caragiannis , Anders Bo Ipsen , Alexander Søltoft