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In fair division, equitability dictates that each participant receives the same level of utility. In this work, we study equitable allocations of indivisible goods among agents with additive valuations. While prior work has studied…

Computer Science and Game Theory · Computer Science 2019-05-28 Rupert Freeman , Sujoy Sikdar , Rohit Vaish , Lirong Xia

We study the classical rent division problem, where $n$ agents must allocate $n$ indivisible rooms and split a fixed total rent $R$. The goal is to compute an envy-free (EF) allocation, where no agent prefers another agent's room and rent…

Computer Science and Game Theory · Computer Science 2025-10-08 Rohith Reddy Gangam , Shayan Taherijam , Vijay V. Vazirani

We study the fair allocation of mixtures of indivisible goods and chores under lexicographic preferences$\unicode{x2014}$a subdomain of additive preferences. A prominent fairness notion for allocating indivisible items is envy-freeness up…

Computer Science and Game Theory · Computer Science 2023-05-08 Hadi Hosseini , Aghaheybat Mammadov , Tomasz Wąs

We prove the following results for task allocation of indivisible resources: - The problem of finding a leximin-maximal resource allocation is in P if the agents have max-utility functions and atomic demands. - Deciding whether a resource…

Multiagent Systems · Computer Science 2008-10-17 Bart de Keijzer

We analyze the run-time complexity of computing allocations that are both fair and maximize the utilitarian social welfare, defined as the sum of agents' utilities. We focus on two tractable fairness concepts: envy-freeness up to one item…

Computer Science and Game Theory · Computer Science 2024-09-23 Haris Aziz , Xin Huang , Nicholas Mattei , Erel Segal-Halevi

Fair allocation of indivisible goods studies allocating $m$ goods among $n$ agents in a fair manner. While fairness is a fundamental requirement in many real-world applications, it often conflicts with (economic) efficiency. This raises a…

Computer Science and Game Theory · Computer Science 2025-06-03 Xiaolin Bu , Zihao Li , Shengxin Liu , Jiaxin Song , Biaoshuai Tao

I provide a unified framework to establish the existence of a weak Pareto efficient, envy-free allocation in general settings: random allocations are probability measures on a compact metric space, and preferences of agents are represented…

Theoretical Economics · Economics 2026-05-28 Anna Vakarova

This paper studies a general class of social choice problems in which agents' payoff functions (or types) are privately observable random variables, and monetary transfers are not available. We consider cardinal social choice functions…

Theoretical Economics · Economics 2024-08-20 Kazuya Kikuchi , Yukio Koriyama

We introduce and study the problem of designing optimal contracts under fairness constraints on the task assignments and compensations. We adopt the notion of envy-free (EF) and its relaxations, $\epsilon$-EF and envy-free up to one item…

Computer Science and Game Theory · Computer Science 2025-07-23 Matteo Castiglioni , Junjie Chen , Yingkai Li

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

We consider the egalitarian welfare aspects of random assignment mechanisms when agents have unrestricted cardinal utilities over the objects. We give bounds on how well different random assignment mechanisms approximate the optimal…

Computer Science and Game Theory · Computer Science 2015-07-27 Haris Aziz , Jiashu Chen , Aris Filos-Ratsikas , Simon Mackenzie , Nicholas Mattei

Building fair recommender systems is a challenging and crucial area of study due to its immense impact on society. We extended the definitions of two commonly accepted notions of fairness to recommender systems, namely equality of…

Machine Learning · Statistics 2022-08-12 Preetam Nandy , Cyrus Diciccio , Divya Venugopalan , Heloise Logan , Kinjal Basu , Noureddine El Karoui

Fairly allocating indivisible goods is a frequently occurring task in everyday life. Given an initial allocation of the goods, we consider the problem of reforming it via a sequence of exchanges to attain fairness in the form of…

Computer Science and Game Theory · Computer Science 2024-12-30 Sheung Man Yuen , Ayumi Igarashi , Naoyuki Kamiyama , Warut Suksompong

A fundamental resource allocation setting is the random assignment problem in which agents express preferences over objects that are then randomly allocated to the agents. In 2001, Bogomolnaia and Moulin presented the probabilistic serial…

Computer Science and Game Theory · Computer Science 2016-04-27 Haris Aziz , Pang Luo , Christine Rizkallah

The past few years have seen a surge of work on fairness in allocation problems where items must be fairly divided among agents having individual preferences. In comparison, fairness in settings with preferences on both sides, that is,…

Computer Science and Game Theory · Computer Science 2022-05-26 Shivika Narang , Arpita Biswas , Y Narahari

In fair division of indivisible goods, using sequences of sincere choices (or picking sequences) is a natural way to allocate the objects. The idea is as follows: at each stage, a designated agent picks one object among those that remain.…

Artificial Intelligence · Computer Science 2018-08-01 Aurélie Beynier , Sylvain Bouveret , Michel Lemaître , Nicolas Maudet , Simon Rey

We consider the mechanism design problem of a principal allocating a single good to one of several agents without monetary transfers. Each agent desires the good and uses it to create value for the principal. We designate this value as the…

Theoretical Economics · Economics 2024-06-26 Halil İbrahim Bayrak , Çağıl Koçyiğit , Daniel Kuhn , Mustafa Çelebi Pınar

The fair allocation of indivisible resources is a fundamental problem. Existing research has developed various allocation mechanisms or algorithms to satisfy different fairness notions. For example, round robin (RR) was proposed to meet the…

Artificial Intelligence · Computer Science 2025-05-13 Ryota Maruo , Koh Takeuchi , Hisashi Kashima

We initiate the work on fair and strategyproof allocation of indivisible chores. The fairness concept we consider in this paper is maxmin share (MMS) fairness. We consider three previously studied models of information elicited from the…

Computer Science and Game Theory · Computer Science 2019-05-23 Haris Aziz , Bo Li , Xiaowei Wu

Mechanism design is addressed in the context of fair allocations of indivisible goods with monetary compensation. Motivated by a real-world social choice problem, mechanisms with verification are considered in a setting where (i) agents'…

Computer Science and Game Theory · Computer Science 2012-09-18 Gianluigi Greco , Francesco Scarcello
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