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The classical house allocation problem involves assigning $n$ houses (or items) to $n$ agents according to their preferences. A key criterion in such problems is satisfying some fairness constraints such as envy-freeness. We consider a…

Computer Science and Game Theory · Computer Science 2023-09-20 Hadi Hosseini , Justin Payan , Rik Sengupta , Rohit Vaish , Vignesh Viswanathan

We study fair division of goods under the broad class of generalized assignment constraints. In this constraint framework, the sizes and values of the goods are agent-specific, and one needs to allocate the goods among the agents fairly…

Computer Science and Game Theory · Computer Science 2023-05-03 Siddharth Barman , Arindam Khan , Sudarshan Shyam , K. V. N. Sreenivas

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

In the assignment problem, the goal is to assign indivisible items to agents who have ordinal preferences, efficiently and fairly, in a strategyproof manner. In practice, first-choice maximality, i.e., assigning a maximal number of agents…

Computer Science and Game Theory · Computer Science 2023-01-24 Xiaoxi Guo , Sujoy Sikdar , Lirong Xia , Yongzhi Cao , Hanpin Wang

The problem of allocating indivisible resources to agents arises in a wide range of domains, including treatment distribution and social support programs. An important goal in algorithm design for this problem is fairness, where the focus…

Computer Science and Game Theory · Computer Science 2026-02-17 Niclas Boehmer , Luca Kreisel

We study the problem of Envy-Free Incomplete Connected Fair Division, where exactly p vertices of an undirected graph must be allocated to agents such that each agent receives a connected share and does not envy another agent's share.…

Data Structures and Algorithms · Computer Science 2025-12-30 Ajaykrishnan E S , Daniel Lokshtanov

We study a dynamic matching problem on a two-sided platform with unbalanced patience, in which long-lived supply accumulates over time with a unit waiting cost per period, while short-lived demand departs if not matched promptly. High- or…

Theoretical Economics · Economics 2026-02-05 Zhiyuan Chen , Rui , Chen , Ming Hu , Yun Zhou

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

This paper considers the problem of randomly assigning a set of objects to a set of agents based on the ordinal preferences of agents. We generalize the well-known immediate acceptance algorithm to the afore-mentioned random environments…

Theoretical Economics · Economics 2021-04-20 Yajing Chen , Patrick Harless , Zhenhua Jiao

We study the problem of partitioning a set of agents into coalitions based on the agents' additively separable preferences, which can also be viewed as a hedonic game. We apply three successively weaker solution concepts, namely…

Computer Science and Game Theory · Computer Science 2024-08-06 Michael McKay , Ágnes Cseh , David Manlove

We consider a fair division setting where indivisible items are allocated to agents. Each agent in the setting has strictly negative, zero or strictly positive utility for each item. We, thus, make a distinction between items that are good…

Computer Science and Game Theory · Computer Science 2020-05-14 Martin Aleksandrov

We investigate Ekici (2024b)'s multi-center allocation problems, focusing on fairness in this context. We introduce three fairness notions that respect centers' priorities: internal fairness, external fairness, and procedural fairness. The…

Theoretical Economics · Economics 2026-03-03 Yao Cheng , Di Feng

The airport game is a classical and well-known model of fair cost-sharing for a single facility among multiple agents. This paper extends it to the so-called assignment setting, that is, for multiple facilities and agents, each agent…

Computer Science and Game Theory · Computer Science 2021-05-06 Yuki Amano , Ayumi Igarashi , Yasushi Kawase , Kazuhisa Makino , Hirotaka Ono

Classic cake-cutting algorithms enable people with different preferences to divide among them a heterogeneous resource (``cake''), such that the resulting division is fair according to each agent's individual preferences. However, these…

Computer Science and Game Theory · Computer Science 2021-08-06 Erel Segal-Halevi , Shmuel Nitzan , Avinatan Hassidim , Yonatan Aumann

We study the fair allocation of indivisible goods among agents with identical, additive valuations but individual budget constraints. Here, the indivisible goods--each with a specific size and value--need to be allocated such that the…

Computer Science and Game Theory · Computer Science 2023-03-20 Siddharth Barman , Arindam Khan , Sudarshan Shyam , K. V. N. Sreenivas

In classic fair division problems such as cake cutting and rent division, envy-freeness requires that each individual (weakly) prefer his allocation to anyone else's. On a conceptual level, we argue that envy-freeness also provides a…

Machine Learning · Computer Science 2020-09-25 Maria-Florina Balcan , Travis Dick , Ritesh Noothigattu , Ariel D. Procaccia

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

We study the problem of fairly allocating indivisible goods to agents in an online setting, where goods arrive sequentially and must be allocated irrevocably. Focusing on the popular fairness notions of envy-freeness, proportionality, and…

Computer Science and Game Theory · Computer Science 2026-05-29 Tzeh Yuan Neoh , Jannik Peters , Nicholas Teh

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 consider the classic problem of envy-free division of a heterogeneous good ("cake") among several agents. It is known that, when the allotted pieces must be connected, the problem cannot be solved by a finite algorithm for 3 or more…

Data Structures and Algorithms · Computer Science 2018-05-15 Erel Segal-Halevi , Avinatan Hassidim , Yonatan Aumann
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