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We study the problem of computing maximin share guarantees, a recently introduced fairness notion. Given a set of $n$ agents and a set of goods, the maximin share of a single agent is the best that she can guarantee to herself, if she would…

Computer Science and Game Theory · Computer Science 2018-06-12 Georgios Amanatidis , Evangelos Markakis , Afshin Nikzad , Amin Saberi

We study the maximin share (MMS) fair allocation of $m$ indivisible chores to $n$ agents who have costs for completing the assigned chores. It is known that exact MMS fairness cannot be guaranteed, and so far the best-known approximation…

Computer Science and Game Theory · Computer Science 2023-05-19 Bo Li , Fangxiao Wang , Yu Zhou

We consider the problem of allocating indivisible goods fairly among n agents who have additive and submodular valuations for the goods. Our fairness guarantees are in terms of the maximin share, that is defined to be the maximum value that…

Computer Science and Game Theory · Computer Science 2020-04-07 Siddharth Barman , Sanath Kumar Krishnamurthy

The problem of fair division of indivisible goods has been receiving much attention recently. The prominent metric of envy-freeness can always be satisfied in the divisible goods setting (see for example \cite{BT95}), but often cannot be…

Computer Science and Game Theory · Computer Science 2022-10-26 Kevin Hsu

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 a set of indivisible items to a set of agents with additive valuations. Recently, Feige et al. (WINE'21) proved that a maximin share (MMS) allocation exists for all instances with $n$ agents and no…

Computer Science and Game Theory · Computer Science 2023-02-02 Halvard Hummel

This work addresses fair allocation of indivisible items in settings wherein it is feasible to create copies of resources or dispose of tasks. We establish that exact maximin share (MMS) fairness can be achieved via limited duplication of…

Computer Science and Game Theory · Computer Science 2025-03-18 Siddharth Barman , Satyanand Rammohan , Aditi Sethia

We study the problem of allocating $m$ indivisible chores to $n$ agents with additive cost functions under the fairness notion of maximin share (MMS). In this work, we propose a notion called $\alpha$-approximate all-but-one maximin share…

Computer Science and Game Theory · Computer Science 2024-10-17 Jiawei Qiu , Xiaowei Wu , Cong Zhang , Shengwei Zhou

We study truthful mechanisms for approximating the Maximin-Share (MMS) allocation of agents with additive valuations for indivisible goods. Algorithmically, constant factor approximations exist for the problem for any number of agents. When…

Computer Science and Game Theory · Computer Science 2024-06-12 Ilan Reuven Cohen , Alon Eden , Talya Eden , Arsen Vasilyan

We study a fundamental fair allocation problem, where the agent's value is determined by the number of bins either used to pack or cover the items allocated to them. Fairness is evaluated using the maximin share (MMS) criterion. This…

Computer Science and Game Theory · Computer Science 2025-10-07 Bo Li , Ankang Sun , Zunyu Wang , Yu Zhou

We study the fair allocation of indivisible chores among agents with asymmetric weights. Among the various fairness notions, weighted maximin share (WMMS) stands out as particularly compelling. However, whether WMMS admits a constant-factor…

Computer Science and Game Theory · Computer Science 2025-10-09 Bo Li , Fangxiao Wang , Shiji Xing

We study the fair allocation of indivisible goods among agents with additive valuations. The fair division literature has traditionally focused on two broad classes of fairness notions: envy-based notions and share-based notions. Within the…

Computer Science and Game Theory · Computer Science 2026-04-24 Hannaneh Akrami , Timo Reichert

We consider the problem of fairly allocating a set of indivisible items under the criteria of the maximin share guarantee. Specifically, we study approximation of maximin share allocations under hereditary set system valuations, in which…

Computer Science and Game Theory · Computer Science 2024-04-18 Halvard Hummel

We consider allocations of a set of $m$ indivisible goods to $n$ agents of equal entitlements that have valuations from the class XOS. A previous sequence of works showed allocations that obtain an $\alpha$-approximation for the maximin…

Computer Science and Game Theory · Computer Science 2026-05-12 Uriel Feige , Vadim Grinberg

We consider the problem of fair allocation of indivisible goods to $n$ agents, with no transfers. When agents have equal entitlements, the well established notion of the maximin share (MMS) serves as an attractive fairness criterion, where…

Computer Science and Game Theory · Computer Science 2021-11-16 Moshe Babaioff , Tomer Ezra , Uriel Feige

We investigate fairness in the allocation of indivisible items among groups of agents using the notion of maximin share (MMS). While previous work has shown that no nontrivial multiplicative MMS approximation can be guaranteed in this…

Computer Science and Game Theory · Computer Science 2025-03-06 Pasin Manurangsi , Warut Suksompong

We study the problem of fairly allocating indivisible goods to a set of agents with additive leveled valuations. A valuation function is called leveled if and only if bundles of larger size have larger value than bundles of smaller size.…

Computer Science and Game Theory · Computer Science 2024-10-04 Mahyar Afshinmehr , Mehrafarin Kazemi , Kurt Mehlhorn

We study the problem of fair allocation of indivisible goods for subadditive agents. While constant-\textsf{MMS} bounds have been given for additive and fractionally subadditive agents, the best existential bound for the case of subadditive…

Computer Science and Game Theory · Computer Science 2025-06-09 Masoud Seddighin , Saeed Seddighin

We study the problem of fairly allocating a set of m indivisible chores (items with non-positive value) to n agents. We consider the desirable fairness notion of 1-out-of-d maximin share (MMS) -- the minimum value that an agent can…

Computer Science and Game Theory · Computer Science 2022-01-20 Hadi Hosseini , Andrew Searns , Erel Segal-Halevi

We study the problem of (approximate) maximin share (MMS) allocation of indivisible items among a set of agents. We focus on the graphical valuation model, previously studied by Christodolou, Fiat, Koutsoupias, and Sgouritsa ("Fair…

Computer Science and Game Theory · Computer Science 2026-05-08 George Christodoulou , Symeon Mastrakoulis