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We study the problem of fairly dividing indivisible goods among a set of agents under the fairness notion of Any Price Share (APS). APS is known to dominate the widely studied Maximin share (MMS). Since an exact APS allocation may not…

Computer Science and Game Theory · Computer Science 2023-12-15 Pooja Kulkarni , Rucha Kulkarni , Ruta Mehta

We consider the fair division problem of indivisible items. It is well-known that an envy-free allocation may not exist, and a relaxed version of envy-freeness, envy-freeness up to one item (EF1), has been widely considered. In an EF1…

Computer Science and Game Theory · Computer Science 2022-11-30 Xiaolin Bu , Zihao Li , Shengxin Liu , Jiaxin Song , Biaoshuai Tao

Fairness is well studied in the context of resource allocation. Researchers have proposed various fairness notions like envy-freeness (EF), and its relaxations, proportionality and max-min share (MMS). There is vast literature on the…

Computer Science and Game Theory · Computer Science 2021-12-15 Manisha Padala , Sujit Gujar

We study the problem of finding fair and efficient allocations of a set of indivisible items to a set of agents, where each item may be a good (positively valued) for some agents and a bad (negatively valued) for others, i.e., a mixed…

Computer Science and Game Theory · Computer Science 2022-02-08 Vasilis Livanos , Ruta Mehta , Aniket Murhekar

We study the fair allocation of indivisible goods with variable groups. In this model, the goal is to partition the agents into groups of given sizes and allocate the goods to the groups in a fair manner. We show that for any number of…

Computer Science and Game Theory · Computer Science 2025-11-11 Paul Gölz , Ayumi Igarashi , Pasin Manurangsi , Warut Suksompong

We study the problem of determining an envy-free allocation of indivisible goods among multiple agents with additive valuations. EFX, which stands for envy-freeness up to any good, is a well-studied relaxation of the envy-free allocation…

Computer Science and Game Theory · Computer Science 2025-01-03 Pratik Ghosal , Vishwa Prakash HV , Prajakta Nimbhorkar , Nithin Varma

We study the fair allocation problem of indivisible items with subsidy. In this paper, we focus on the notion of fairness - equitability (EQ), which requires that items be allocated such that all agents value the bundle they receive…

Computer Science and Game Theory · Computer Science 2025-09-10 Yuanyuan Wang , Tianze Wei

We study fair allocation of indivisible goods and chores among agents with \emph{lexicographic} preferences -- a subclass of additive valuations. In sharp contrast to the goods-only setting, we show that an allocation satisfying…

Computer Science and Game Theory · Computer Science 2022-03-15 Hadi Hosseini , Sujoy Sikdar , Rohit Vaish , Lirong Xia

A set of objects is to be divided fairly among agents with different tastes, modeled by additive utility-functions. If we consider the objects as indivisible, many instances of the decision problem: ``Is there a fair division of the objects…

Computer Science and Game Theory · Computer Science 2025-07-03 Samuel Bismuth , Ivan Bliznets , 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

The existence of EFX allocations is a central open problem in discrete fair division. An allocation is EFX (envy-free up to any good) if no agent envies another agent after the removal of any single good from the other agent's bundle. We…

Computer Science and Game Theory · Computer Science 2026-05-15 Hannaneh Akrami , Alexander Mayorov , Kurt Mehlhorn , Shreyas Srinivas , Christoph Weidenbach

Fair allocation of indivisible goods is a well-explored problem. Traditionally, research focused on individual fairness - are individual agents satisfied with their allotted share? - and group fairness - are groups of agents treated fairly?…

Computer Science and Game Theory · Computer Science 2023-02-15 Jonathan Scarlett , Nicholas Teh , Yair Zick

Our work studies the fair allocation of indivisible items to a set of agents, and falls within the scope of establishing improved approximation guarantees. It is well known by now that the classic solution concepts in fair division, such as…

Computer Science and Game Theory · Computer Science 2023-08-10 Evangelos Markakis , Christodoulos Santorinaios

We study the fair allocation of indivisible items for groups of agents from the perspectives of the agents and a centralized allocator. In our setting, the centralized allocator is interested in ensuring the allocation is fair among the…

Computer Science and Game Theory · Computer Science 2025-11-12 Ying Wang , Jiaqian Li , Tianze Wei , Hau Chan , Minming Li

We study the fundamental problem of allocating indivisible goods to agents with additive preferences. We consider eliciting from each agent only a ranking of her $k$ most preferred goods instead of her full cardinal valuations. We…

Computer Science and Game Theory · Computer Science 2021-05-25 Daniel Halpern , Nisarg Shah

The theory of algorithmic fair allocation is within the center of multi-agent systems and economics in the last decade due to its industrial and social importance. At a high level, the problem is to assign a set of items that are either…

Computer Science and Game Theory · Computer Science 2022-02-18 Haris Aziz , Bo Li , Herve Moulin , Xiaowei Wu

We consider the problem of fair allocation of $m$ indivisible items to $n$ agents with monotone subadditive valuations. For integer $d \ge 2$, a $d$-multi-allocation is an allocation in which each item is allocated to at most $d$ different…

Computer Science and Game Theory · Computer Science 2025-06-27 Uriel Feige

We consider the problem of fairly allocating a set of indivisible goods to a set of strategic agents with additive valuation functions. We assume no monetary transfers and, therefore, a mechanism in our setting is an algorithm that takes as…

Computer Science and Game Theory · Computer Science 2023-12-12 Georgios Amanatidis , Georgios Birmpas , Federico Fusco , Philip Lazos , Stefano Leonardi , Rebecca Reiffenhäuser

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 present a simple local search algorithm for computing EFX (envy-free up to any good) allocations of $m$ indivisible goods among $n$ agents with additive valuations. EFX is a compelling fairness notion, and whether such allocations always…

Computer Science and Game Theory · Computer Science 2025-10-08 Simina Brânzei