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In fair division applications, agents may have unequal entitlements reflecting their different contributions. Moreover, the contributions of agents may depend on the allocation itself. Previous fairness notions designed for agents with…

Computer Science and Game Theory · Computer Science 2023-01-31 Qishen Han , Biaoshuai Tao , Lirong Xia

The goal of fair division is to distribute resources among competing players in a "fair" way. Envy-freeness is the most extensively studied fairness notion in fair division. Envy-free allocations do not always exist with indivisible goods,…

Computer Science and Game Theory · Computer Science 2017-11-15 Benjamin Plaut , Tim Roughgarden

Ensuring efficiency and envy-freeness in allocating indivisible goods without money often requires randomization. However, existing combinatorial assignment mechanisms (for applications such as course allocation, food banks, and refugee…

Theoretical Economics · Economics 2025-10-03 Thành Nguyen , Alexander Teytelboym , Shai Vardi

We study temporal fair division, whereby a set of agents are allocated a (possibly different) set of goods on each day for a period of days. We study this setting, as well as a number of its special cases formed by the restrictions to two…

Computer Science and Game Theory · Computer Science 2024-11-01 Benjamin Cookson , Soroush Ebadian , Nisarg Shah

We study the fair allocation of indivisible goods under cardinality constraints, where each agent must receive a bundle of fixed size. This models practical scenarios, such as assigning shifts or forming equally sized teams. Recently,…

Computer Science and Game Theory · Computer Science 2025-07-29 Alviona Mancho , Evangelos Markakis , Nicos Protopapas

We consider the problem of allocating heterogeneous and indivisible goods among strategic agents, with preferences over subsets of goods, when there is no medium of exchange. This model captures the well studied problem of fair allocation…

Computer Science and Game Theory · Computer Science 2026-04-27 Moshe Babaioff , Noam Manaker Morag

We study the problem of fairly allocating $m$ indivisible goods to $n$ agents, where agents may have different preferences over the goods. In the traditional setting, agents' valuations are provided as inputs to the algorithm. In this…

Computer Science and Game Theory · Computer Science 2025-08-05 Xiaolin Bu , Zihao Li , Shengxin Liu , Jiaxin Song , Biaoshuai Tao

Finding an envy-free allocation of indivisible resources to agents is a central task in many multiagent systems. Often, non-trivial envy-free allocations do not exist, and, when they do, finding them can be computationally hard. Classical…

Computer Science and Game Theory · Computer Science 2020-11-24 Robert Bredereck , Andrzej Kaczmarczyk , Rolf Niedermeier

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

We study the problem of fairly allocating indivisible goods to groups of agents. Agents in the same group share the same set of goods even though they may have different preferences. Previous work has focused on unanimous fairness, in which…

Computer Science and Game Theory · Computer Science 2020-01-01 Erel Segal-Halevi , Warut Suksompong

In the assignment problem, a set of items must be allocated to unit-demand agents who express ordinal preferences (rankings) over the items. In the assignment problem with priorities, agents with higher priority are entitled to their…

Computer Science and Game Theory · Computer Science 2023-02-01 Zeyu Shen , Zhiyi Wang , Xingyu Zhu , Brandon Fain , Kamesh Munagala

We study the question of dividing a collection of indivisible goods amongst a set of agents. The main objective of research in the area is to achieve one of two goals: fairness or efficiency. On the fairness side, envy-freeness is the…

Computer Science and Game Theory · Computer Science 2021-06-03 Vishnu V. Narayan , Mashbat Suzuki , Adrian Vetta

This work is motivated by a common urban renewal process called Reconstruct and Divide. It involves the demolition of old buildings and the construction of new ones. Original homeowners are compensated with upgraded apartments, while…

Computer Science and Game Theory · Computer Science 2026-02-23 Noga Klein Elmalem , Rica Gonen , Erel Segal-Halevi

We consider a multi-agent resource allocation setting in which an agent's utility may decrease or increase when an item is allocated. We take the group envy-freeness concept that is well-established in the literature and present stronger…

Computer Science and Game Theory · Computer Science 2019-07-23 Haris Aziz , Simon Rey

We study the fair allocation of a cake, which serves as a metaphor for a divisible resource, under the requirement that each agent should receive a contiguous piece of the cake. While it is known that no finite envy-free algorithm exists in…

Computer Science and Game Theory · Computer Science 2020-09-24 Paul W. Goldberg , Alexandros Hollender , Warut Suksompong

We study the mechanism design problem of allocating a set of indivisible items without monetary transfers. Despite the vast literature on this very standard model, it still remains unclear how do truthful mechanisms look like. We focus on…

Computer Science and Game Theory · Computer Science 2017-05-31 Georgios Amanatidis , Georgios Birmpas , George Christodoulou , Evangelos Markakis

We study a resource allocation setting where $m$ discrete items are to be divided among $n$ agents with additive utilities, and the agents' utilities for individual items are drawn at random from a probability distribution. Since common…

Computer Science and Game Theory · Computer Science 2023-03-20 Pasin Manurangsi , Warut Suksompong

We study how to fairly allocate a set of indivisible chores to a group of agents, where each agent $i$ has a non-negative weight $w_i$ that represents its obligation for undertaking the chores. We consider the fairness notion of weighted…

Computer Science and Game Theory · Computer Science 2023-01-20 Xiaowei Wu , Cong Zhang , Shengwei Zhou

We study the problem of fairly allocating $m$ indivisible items among $n$ agents. Envy-free allocations, in which each agent prefers her bundle to the bundle of every other agent, need not exist in the worst case. However, when agents have…

Computer Science and Game Theory · Computer Science 2023-07-20 Gerdus Benadè , Daniel Halpern , Alexandros Psomas , Paritosh Verma

We study the problem of fairly and efficiently allocating a set of items among strategic agents with additive valuations, where items are either all indivisible or all divisible. When items are goods, numerous positive and negative results…

Computer Science and Game Theory · Computer Science 2025-07-08 Bo Li , Biaoshuai Tao , Fangxiao Wang , Xiaowei Wu , Mingwei Yang , Shengwei Zhou