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Fair division is a fundamental problem in various multi-agent settings, where the goal is to divide a set of resources among agents in a fair manner. We study the case where m indivisible items need to be divided among n agents with…

Computer Science and Game Theory · Computer Science 2021-04-07 Jugal Garg , Setareh Taki

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 consider fair division of a set of indivisible goods among $n$ agents with additive valuations using the fairness notion of maximin share (MMS). MMS is the most popular share-based notion, in which an agent finds an allocation fair to…

Computer Science and Game Theory · Computer Science 2024-02-19 Hannaneh Akrami , Jugal Garg , Eklavya Sharma , Setareh Taki

We study fair division of indivisible goods under the maximin share (MMS) fairness criterion in settings where agents are grouped into a small number of types, with agents within each type having identical valuations. For the special case…

Computer Science and Game Theory · Computer Science 2025-03-05 Jugal Garg , Parnian Shahkar

We study the problem of allocating indivisible goods among n agents in a fair manner. For this problem, maximin share (MMS) is a well-studied solution concept which provides a fairness threshold. Specifically, maximin share is defined as…

Computer Science and Game Theory · Computer Science 2017-11-22 Siddharth Barman , Arpita Biswas , Sanath Kumar Krishnamurthy , Y. Narahari

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

We study the problem of fairly allocating indivisible goods when limited sharing is allowed, that is, each good may be allocated to up to $k$ agents, while incurring a cost for sharing. While classic maximin share (MMS) allocations may not…

Computer Science and Game Theory · Computer Science 2026-03-05 Hana Salavcova , Martin Černý , Arpita Biswas

We study the problem of fairly allocating a set of indivisible items among a set of agents. We consider the notion of (approximate) maximin share (MMS) and we provide an improved lower bound of $1/2$ (which is tight) for the case of…

Computer Science and Game Theory · Computer Science 2025-02-10 George Christodoulou , Vasilis Christoforidis , Symeon Mastrakoulis , Alkmini Sgouritsa

In fair division of indivisible goods, $\ell$-out-of-$d$ maximin share (MMS) is the value that an agent can guarantee by partitioning the goods into $d$ bundles and choosing the $\ell$ least preferred bundles. Most existing works aim to…

Computer Science and Game Theory · Computer Science 2022-05-30 Hadi Hosseini , Andrew Searns , Erel Segal-Halevi

The maximin share ($\textsf{MMS}$) is the most prominent share-based fairness notion in the fair allocation of indivisible goods. Recent years have seen significant efforts to improve the approximation guarantees for $\textsf{MMS}$ for…

Computer Science and Game Theory · Computer Science 2025-10-14 Ehsan Heidari , Alireza Kaviani , Masoud Seddighin , AmirMohammad Shahrezaei

We study fair resource allocation when the resources contain a mixture of divisible and indivisible goods, focusing on the well-studied fairness notion of maximin share fairness (MMS). With only indivisible goods, a full MMS allocation may…

Computer Science and Game Theory · Computer Science 2021-07-02 Xiaohui Bei , Shengxin Liu , Xinhang Lu , Hongao Wang

We study the fundamental problem of fairly allocating a set of indivisible goods among $n$ agents with additive valuations using the desirable fairness notion of maximin share (MMS). MMS is the most popular share-based notion, in which an…

Computer Science and Game Theory · Computer Science 2023-07-25 Hannaneh Akrami , Jugal Garg

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

We study the problem of fair allocation of a set of indivisible items among agents with additive valuations, under cardinality constraints. In this setting, the items are partitioned into categories, each with its own limit on the number of…

Computer Science and Game Theory · Computer Science 2022-08-11 Halvard Hummel , Magnus Lie Hetland

We study the fair division of indivisible items among $n$ agents with heterogeneous additive valuations, subject to lower and upper quotas on the number of items allocated to each agent. Such constraints are crucial in various applications,…

Computer Science and Game Theory · Computer Science 2026-02-10 Hirota Kinoshita , Ayumi Igarashi

We consider the problem of approximate maximin share (MMS) allocation of indivisible items among three agents with additive valuation functions. For goods, we show that an $\frac{11}{12}$ - MMS allocation always exists, improving over the…

Computer Science and Game Theory · Computer Science 2022-05-12 Uriel Feige , Alexey Norkin

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 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 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 study the problem of fairly allocating indivisible goods among a set of agents. Our focus is on the existence of allocations that give each agent their maximin fair share--the value they are guaranteed if they divide the goods into as…

Computer Science and Game Theory · Computer Science 2024-07-19 Sirin Botan , Angus Ritossa , Mashbat Suzuki , Toby Walsh
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