相关论文: Envy-free division via configuration spaces

We study a fair resource sharing problem, where a set of resources are to be shared among a group of agents. Each agent demands one resource and each resource can serve a limited number of agents. An agent cares about what resource they get…

We study competition on scale-free random graphs, where the degree distribution satisfies an asymptotic power-law with infinite variance. Our competition process is such that the two types attempt at occupying vertices incident to the…

We study classic fair-division problems in a partial information setting. This paper respectively addresses fair division of rent, cake, and indivisible goods among agents with cardinal preferences. We will show that, for all of these…

We introduce a version of Farber's topological complexity suitable for investigating mechanical systems whose configuration spaces exhibit symmetries. Our invariant has vastly different properties to the previous approaches of Colman-Grant,…

In this paper, we focus on how to dynamically allocate a divisible resource fairly among n players who arrive and depart over time. The players may have general heterogeneous valuations over the resource. It is known that the exact…

We extend the notion of combinatorial discrepancy to \emph{non-additive} functions. Our main result is an upper bound of $O(\sqrt{n \log(nk)})$ on the non-additive $k$-color discrepancy when $k$ is a prime power. We demonstrate two…

Envy-Freeness is one of the most fundamental and important concepts in fair allocation. Some recent studies have focused on the concept of weighted envy-freeness. Under this concept, each agent is assigned a weight, and their valuations are…

We study the problem of allocating a set of indivisible chores to three agents, among whom two have additive cost functions, in a fair manner. Two fairness notions under consideration are envy-freeness up to any chore (EFX) and a relaxed…

We study the query complexity of cake cutting and give lower and upper bounds for computing approximately envy-free, perfect, and equitable allocations with the minimum number of cuts. The lower bounds are tight for computing connected…

Shape(-and-scale) spaces - configuration spaces for generalized Kendall-type Shape(-and-Scale) Theories - are usually not manifolds but stratified manifolds. While in Kendall's own case - similarity shapes - the shape spaces are…

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…

In this thesis we propose and study a theory of ordered locales, a type of point-free space equipped with a preorder structure on its frame of opens. It is proved that the Stone-type duality between topological spaces and locales lifts to a…

In this work we give a tight lower bound on makespan approximations for envy-free allocation mechanism dedicated to scheduling tasks on unrelated machines. Specifically, we show that no mechanism exists that can guarantee an envy-free…

We study the classical rent division problem, where $n$ agents must allocate $n$ indivisible rooms and split a fixed total rent $R$. The goal is to compute an envy-free (EF) allocation, where no agent prefers another agent's room and rent…

We consider stability concepts for random matchings where agents have preferences over objects and objects have priorities for the agents. When matchings are deterministic, the standard stability concept also captures the fairness property…

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…

Fairly dividing a set of indivisible resources to a set of agents is of utmost importance in some applications. However, after an allocation has been implemented the preferences of agents might change and envy might arise. We study the…

The current practice of envy-free rent division, lead by the fair allocation website Spliddit, is based on quasi-linear preferences. These preferences rule out agents' well documented financial constraints. To resolve this issue we consider…

We consider the classical cake-cutting problem where we wish to fairly divide a heterogeneous resource, often modeled as a cake, among interested agents. Work on the subject typically assumes that the cake is represented by an interval. In…

We study the problem of fair cake-cutting where each agent receives a connected piece of the cake. A division of the cake is deemed fair if it is equitable, which means that all agents derive the same value from their assigned piece. Prior…