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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,…
Envy-freeness up to one good (EF1) is a well-studied fairness notion for indivisible goods that addresses pairwise envy by the removal of at most one good. In the worst case, each pair of agents might require the (hypothetical) removal of a…
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…
We explore the fair distribution of a set of $m$ indivisible chores among $n$ agents, where each agent's costs are evaluated using a monotone cost function. Our focus lies on two fairness criteria: envy-freeness up to any item (EFX) and a…
We study the fair division problem and the existence of allocations satisfying the fairness criterion envy-freeness up to any item (EFX). The existence of EFX allocations is a major open problem in the fair division literature. We consider…
We introduce a model of fair division with market values, where indivisible goods must be partitioned among agents with (additive) subjective valuations, and each good additionally has a market value. The market valuation can be viewed as a…
We study the problem of allocating indivisible items to budget-constrained agents, aiming to provide fairness and efficiency guarantees. Specifically, our goal is to ensure that the resulting allocation is envy-free up to any item (EFx)…
We study the problem of fairly and truthfully allocating $m$ indivisible items to $n$ agents with additive preferences. Specifically, we consider truthful mechanisms outputting allocations that satisfy EF$^{+u}_{-v}$, where, in an…
The problem of fairly allocating a set of indivisible items is a well-known challenge in the field of (computational) social choice. In this scenario, there is a fundamental incompatibility between notions of fairness (such as envy-freeness…
We study fair division of indivisible items under a variable input setting, where the set of agents or items may change over time. Starting from an arbitrary allocation, the goal is to restore envy-freeness up to one item (EF1) through item…
One of the most important topics in discrete fair division is whether an EFX allocation exists for any instance. Although the existence of EFX allocations is a standing open problem for both goods and chores, the understanding of the…
We consider the complexity of finding envy-free allocations for the class of graphical valuations. Graphical valuations were introduced by Christodoulou et. al.(2023) as a structured class of valuations that admit allocations that are…
We consider the fair allocation of indivisible items to several agents and add a graph theoretical perspective to this classical problem. Namely, we introduce an incompatibility relation between pairs of items described in terms of a…
We study a discrete fair division problem where $n$ agents have additive valuation functions over a set of $m$ goods. We focus on the well-known $\alpha$-EFX fairness criterion, according to which the envy of an agent for another agent is…
Since its introduction, envy-freeness up to any good (EFX) has become a fundamental solution concept in fair division of indivisible goods. Its existence remains elusive -- even for four agents with additive utility functions, it is unknown…
\textit{Fair division} of resources among competing agents is a fundamental problem in computational social choice and economic game theory. It has been intensively studied on various kinds of items (\textit{divisible} and…
We study the allocation of indivisible goods that form an undirected graph and quantify the loss of fairness when we impose a constraint that each agent must receive a connected subgraph. Our focus is on well-studied fairness notions…
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.…
This paper re-examines the problem of fairly and efficiently allocating indivisible goods among agents with additive bivalued valuations. Garg and Murhekar (2021) proposed a polynomial-time algorithm that purported to find an EFX and fPO…
In the allocation of indivisible goods, a prominent fairness notion is envy-freeness up to one good (EF1). We initiate the study of reachability problems in fair division by investigating the problem of whether one EF1 allocation can be…