Fair Division Through Information Withholding

Hosseini, Hadi; Sikdar, Sujoy; Vaish, Rohit; Wang, Hejun; Xia, Lirong

doi:10.1609/aaai.v34i02.5573

Cited by 18 publications

(22 citation statements)

References 16 publications

(24 reference statements)

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“…We show that the problem of finding locally EEF allocations is W [1]-hard when parameterized by the vertex cover number (Theorem 8). We remark that a stronger hardness result can be observed for the closely related parameter of twin cover 5 -indeed, the known NP-hardness of finding envy-free allocations for binary valuations on complete graphs [15,3] implies hardness for graphs that have a twin cover of size zero.…”

Section: Structural Parameters Ii: Vertex Cover and Twin Covermentioning

confidence: 79%

“…Here, the notions of fairness localized according to the graph, and the network also constraints the exchanges that can take place -agents can engage in an exchange only if they are friends in the network. There are also some lines of work that suggest eliminating envy by some mechanism for hiding information [15].…”

Section: Related Workmentioning

confidence: 99%

“…Although Beynier et al [5] also show hardness results for very sparse graphs, we note that our methods are significantly different since the models for the valuations are different and additionally, the allocations we seek need not give every agent exactly one item. Moving away from sparsity, we recall that finding complete envy-free allocations for binary valuations is known to be NP-hard even for complete graphs [15,3], which justifies the need for using additional parameters 2 in the XP 3 algorithm for finding locally envy-free allocations shown by [14,Theorem 10].…”

Section: Sparse and Dense Graphsmentioning

confidence: 99%

See 2 more Smart Citations

On Fair Division with Binary Valuations Respecting Social Networks

Misra¹,

Nayak²

2021

Preprint

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We study the computational complexity of finding fair allocations of indivisible goods in the setting where a social network on the agents is given. Notions of fairness in this context are "localized", that is, agents are only concerned about the bundles allocated to their neighbors, rather than every other agent in the system. We comprehensively address the computational complexity of finding locally envy-free and Pareto efficient allocations in the setting where the agents have binary valuations for the goods and the underlying social network is modeled by an undirected graph. We study the problem in the framework of parameterized complexity.We show that the problem is computationally intractable even in fairly restricted scenarios, for instance, even when the underlying graph is a path. We show NP-hardness for settings where the graph has only two distinct valuations among the agents. We demonstrate W-hardness with respect to the number of goods or the size of the vertex cover of the underlying graph. We also consider notions of proportionality that respect the structure of the underlying graph and show that two natural versions of this notion have different complexities: allocating according to the notion that accounts for locality to the greatest degree turns out to be computationally intractable, while for other notions, the allocation problem can be modeled as a structured ILP which can be solved efficiently. ACM Subject ClassificationTheory of computation → Design and analysis of algorithms; Theory of computation → Social networks

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Section: Structural Parameters Ii: Vertex Cover and Twin Covermentioning

confidence: 79%

Section: Related Workmentioning

confidence: 99%

Section: Sparse and Dense Graphsmentioning

confidence: 99%

See 1 more Smart Citation

On Fair Division with Binary Valuations Respecting Social Networks

Misra¹,

Nayak²

2021

Preprint

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“…Aziz et al [2] investigated a model where the information that agents obtain on the allocation is based on a graph representing social contacts. Hosseini et al [18] have proposed an algorithm that eliminates envy through withholding information about a set of few items. Halpern and Shah [16] have also examined the possibilities for overcoming envy by subsidies where agents receive monetary compensation.…”

Section: Related Workmentioning

confidence: 99%

Obtaining a Proportional Allocation by Deleting Items

2021

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We 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

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“…Fair division deals with the allocation of a set of resources to a set of agents in a fair manner (Brams and Taylor, 1996;Foley, 1967;Hosseini et al, 2020). One of its most notable application domains deals with the allocation of indivisible (and non-shareable) goods.…”

Section: Introductionmentioning

confidence: 99%

Guaranteeing Maximin Shares: Some Agents Left Behind

Hosseini¹,

Searns²

2021

Preprint

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The maximin share (MMS) guarantee is a desirable fairness notion for allocating indivisible goods. While MMS allocations do not always exist, several approximation techniques have been developed to ensure that all agents receive a fraction of their maximin share. We focus on an alternative approximation notion, based on the population of agents, that seeks to guarantee MMS for a fraction of agents. We show that no optimal approximation algorithm can satisfy more than a constant number of agents, and discuss the existence and computation of MMS for all but one agent and its relation to approximate MMS guarantees. We then prove the existence of allocations that guarantee MMS for 2 3 of agents, and devise a polynomial time algorithm that achieves this bound for up to nine agents. A key implication of our result is the existence of allocations that guarantee MMS 3n/2 , i.e., the value that agents receive by partitioning the goods into 3 2 n bundles, improving the best known guarantee of MMS 2n−2 . Finally, we provide empirical experiments using synthetic data.

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Fair Division Through Information Withholding

Cited by 18 publications

References 16 publications

On Fair Division with Binary Valuations Respecting Social Networks

On Fair Division with Binary Valuations Respecting Social Networks

Obtaining a Proportional Allocation by Deleting Items

Guaranteeing Maximin Shares: Some Agents Left Behind

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