Fair allocation of indivisible goods: the two-agent case

2012 ◽  
Vol 41 (2) ◽  
pp. 359-380 ◽  
Author(s):  
Eve Ramaekers
Keyword(s):  
Fair Allocation ◽  
Indivisible Goods

Fair Allocation of Indivisible Goods: Beyond Additive Valuations

2021 ◽  
pp. 103633
Author(s):  
Mohammad Ghodsi ◽  
MohammadTaghi HajiAghayi ◽  
Masoud Seddighin ◽  
Saeed Seddighin ◽  
Hadi Yami
Keyword(s):  
Fair Allocation ◽  
Indivisible Goods

scholarly journals Distributed fair allocation of indivisible goods

2017 ◽  
Vol 242 ◽  
pp. 1-22 ◽  
Author(s):  
Yann Chevaleyre ◽  
Ulle Endriss ◽  
Nicolas Maudet
Keyword(s):  
Fair Allocation ◽  
Indivisible Goods

scholarly journals Fair allocation in a general model with indivisible goods

1998 ◽  
Vol 3 (3) ◽  
pp. 195-213 ◽  
Author(s):  
Carmen Beviá
Keyword(s):  
General Model ◽  
Fair Allocation ◽  
Indivisible Goods

scholarly journals Fair Division Under Cardinality Constraints

2018 ◽  
Author(s):  
Arpita Biswas ◽  
Siddharth Barman
Keyword(s):  
Resource Allocation ◽  
Fair Division ◽  
Division Problem ◽  
Fair Allocation ◽  
Indivisible Goods ◽  
Solution Concepts ◽  
Cardinality Constraints ◽  
The Given

We consider the problem of fairly allocating indivisible goods, among agents, under cardinality constraints and additive valuations. In this setting, we are given a partition of the entire set of goods---i.e., the goods are categorized---and a limit is specified on the number of goods that can be allocated from each category to any agent. The objective here is to find a fair allocation in which the subset of goods assigned to any agent satisfies the given cardinality constraints. This problem naturally captures a number of resource-allocation applications, and is a generalization of the well-studied unconstrained fair division problem.  The two central notions of fairness, in the context of fair division of indivisible goods, are envy freeness up to one good (EF1) and the (approximate) maximin share guarantee (MMS). We show that the existence and algorithmic guarantees established for these solution concepts in the unconstrained setting can essentially be achieved under cardinality constraints. Furthermore, focusing on the case wherein all the agents have the same additive valuation, we establish that EF1 allocations exist even under matroid constraints.

Fair Allocation of Indivisible Goods: Improvement

2021 ◽  
Author(s):  
Mohammad Ghodsi ◽  
Mohammad Taghi Hajiaghayi ◽  
Masoud Seddighin ◽  
Saeed Seddighin ◽  
Hadi Yami
Keyword(s):  
Assignment Problem ◽  
Competitive Equilibrium ◽  
Fundamental Problem ◽  
Impossibility Result ◽  
Utility Functions ◽  
Fair Allocation ◽  
Indivisible Goods ◽  
Approximation Result ◽  
Combinatorial Assignment

We study the problem of fair allocation for indivisible goods. We use the maximin share paradigm introduced by Budish [Budish E (2011) The combinatorial assignment problem: Approximate competitive equilibrium from equal incomes. J. Political Econom. 119(6):1061–1103.] as a measure of fairness. Kurokawa et al. [Kurokawa D, Procaccia AD, Wang J (2018) Fair enough: Guaranteeing approximate maximin shares. J. ACM 65(2):8.] were the first to investigate this fundamental problem in the additive setting. They showed that in delicately constructed examples, not everyone can obtain a utility of at least her maximin value. They mitigated this impossibility result with a beautiful observation: no matter how the utility functions are made, we always can allocate the items to the agents to guarantee each agent’s utility is at least 2/3 of her maximin value. They left open whether this bound can be improved. Our main contribution answers this question in the affirmative. We improve their approximation result to a 3/4 factor guarantee.

scholarly journals Obtaining a Proportional Allocation by Deleting Items

Algorithmica ◽  
2021 ◽  
Author(s):  
Britta Dorn ◽  
Ronald de Haan ◽  
Ildikó Schlotter
Keyword(s):  
Control Problem ◽  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Upper Bounds ◽  
Fair Allocation ◽  
Indivisible Goods ◽  
Lower And Upper Bounds ◽  
Proportional Allocation ◽  
Minimum Number

AbstractWe consider the following control problem on fair allocation of indivisible goods. Given a set I of items and a set of agents, each having strict linear preferences over the items, we ask for a minimum subset of the items whose deletion guarantees the existence of a proportional allocation in the remaining instance; we call this problem Proportionality by Item Deletion (PID). Our main result is a polynomial-time algorithm that solves PID for three agents. By contrast, we prove that PID is computationally intractable when the number of agents is unbounded, even if the number k of item deletions allowed is small—we show that the problem is $${\mathsf {W}}[3]$$ W [ 3 ] -hard with respect to the parameter k. Additionally, we provide some tight lower and upper bounds on the complexity of PID when regarded as a function of |I| and k. Considering the possibilities for approximation, we prove a strong inapproximability result for PID. Finally, we also study a variant of the problem where we are given an allocation $$\pi $$ π in advance as part of the input, and our aim is to delete a minimum number of items such that $$\pi $$ π is proportional in the remainder; this variant turns out to be $${{\mathsf {N}}}{{\mathsf {P}}}$$ N P -hard for six agents, but polynomial-time solvable for two agents, and we show that it is $$\mathsf {W[2]}$$ W [ 2 ] -hard when parameterized by the number k of

scholarly journals Fair Allocation of Indivisible Goods to Asymmetric Agents

2019 ◽  
Vol 64 ◽  
pp. 1-20 ◽  
Author(s):  
Alireza Farhadi ◽  
Mohammad Ghodsi ◽  
Mohammad Taghi Hajiaghayi ◽  
Sébastien Lahaie ◽  
David Pennock ◽  
...  
Keyword(s):  
Real World ◽  
Simple Algorithm ◽  
Fair Allocation ◽  
Indivisible Goods ◽  
Real World Data ◽  
The Subject ◽  
Approximation Guarantee ◽  
To Receive ◽  
Positive Results ◽  
Better Than

We study fair allocation of indivisible goods to agents with unequal entitlements. Fair allocation has been the subject of many studies in both divisible and indivisible settings. Our emphasis is on the case where the goods are indivisible and agents have unequal entitlements. This problem is a generalization of the work by Procaccia and Wang (2014) wherein the agents are assumed to be symmetric with respect to their entitlements. Although Procaccia and Wang show an almost fair (constant approximation) allocation exists in their setting, our main result is in sharp contrast to their observation. We show that, in some cases with n agents, no allocation can guarantee better than 1/n approximation of a fair allocation when the entitlements are not necessarily equal. Furthermore, we devise a simple algorithm that ensures a 1/n approximation guarantee. Our second result is for a restricted version of the problem where the valuation of every agent for each good is bounded by the total value he wishes to receive in a fair allocation. Although this assumption might seem without loss of generality, we show it enables us to find a 1/2 approximation fair allocation via a greedy algorithm. Finally, we run some experiments on real-world data and show that, in practice, a fair allocation is likely to exist. We also support our experiments by showing positive results for two stochastic variants of the problem, namely stochastic agents and stochastic items.

scholarly journals Almost Envy-Freeness in Group Resource Allocation

2019 ◽  
Author(s):  
Maria Kyropoulou ◽  
Warut Suksompong ◽  
Alexandros A. Voudouris
Keyword(s):  
Resource Allocation ◽  
Fair Allocation ◽  
Indivisible Goods ◽  
New Model

We study the problem of fairly allocating indivisible goods between groups of agents using the recently introduced relaxations of envy-freeness. We consider the existence of fair allocations under different assumptions on the valuations of the agents. In particular, our results cover cases of arbitrary monotonic, responsive, and additive valuations, while for the case of binary valuations we fully characterize the cardinalities of two groups of agents for which a fair allocation can be guaranteed with respect to both envy-freeness up to one good (EF1) and envy-freeness up to any good (EFX). Moreover, we introduce a new model where the agents are not partitioned into groups in advance, but instead the partition can be chosen in conjunction with the allocation of the goods. In this model, we show that for agents with arbitrary monotonic valuations, there is always a partition of the agents into two groups of any given sizes along with an EF1 allocation of the goods. We also provide an extension of this result to any number of groups.

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