Fair Division Under Cardinality Constraints

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2018/13 ◽

2018 ◽

Cited By ~ 2

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.

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Maximin Share Allocations on Cycles

Journal of Artificial Intelligence Research ◽

10.1613/jair.1.11702 ◽

2020 ◽

Vol 69 ◽

pp. 613-655

Author(s):

Miroslaw Truszczynski ◽

Zbigniew Lonc

Keyword(s):

Resource Allocation ◽

Social Choice ◽

Fundamental Problem ◽

Fair Division ◽

Connected Subgraph ◽

Indivisible Goods ◽

Multi Agent Systems ◽

Agent Systems ◽

Multi Agent ◽

Share Value

The problem of fair division of indivisible goods is a fundamental problem of resource allocation in multi-agent systems, also studied extensively in social choice. Recently, the problem was generalized to the case when goods form a graph and the goal is to allocate goods to agents so that each agent’s bundle forms a connected subgraph. For the maximin share fairness criterion, researchers proved that if goods form a tree, an allocation offering each agent a bundle of at least her maximin share value always exists. Moreover, it can be found in polynomial time. In this paper we consider the problem of maximin share allocations of goods on a cycle. Despite the simplicity of the graph, the problem turns out to be significantly harder than its tree version. We present cases when maximin share allocations of goods on cycles exist and provide in this case results on allocations guaranteeing each agent a certain fraction of her maximin share. We also study algorithms for computing maximin share allocations of goods on cycles.

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Almost Envy-Freeness in Group Resource Allocation

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2019/57 ◽

2019 ◽

Cited By ~ 4

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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Fair Division of a Graph

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2017/20 ◽

2017 ◽

Cited By ~ 11

Author(s):

Sylvain Bouveret ◽

Katarína Cechlárová ◽

Edith Elkind ◽

Ayumi Igarashi ◽

Dominik Peters

Keyword(s):

Simple Structure ◽

Fair Division ◽

Fair Allocation ◽

Connected Subgraph ◽

Solution Concepts ◽

Accessibility Relation ◽

Acyclic Graphs ◽

Special Cases ◽

Additive Utilities ◽

The Relationship

We consider fair allocation of indivisible items under an additional constraint: there is an undirected graph describing the relationship between the items, and each agent's share must form a connected subgraph of this graph. This framework captures, e.g., fair allocation of land plots, where the graph describes the accessibility relation among the plots. We focus on agents that have additive utilities for the items, and consider several common fair division solution concepts, such as proportionality, envy-freeness and maximin share guarantee. While finding good allocations according to these solution concepts is computationally hard in general, we design efficient algorithms for special cases wherethe underlying graph has simple structure, and/or the number of agents---or, less restrictively, the number of agent types---is small. In particular, despite non-existence results in the general case, we prove that for acyclic graphs a maximin share allocation always exists and can be found efficiently.

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Almost Group Envy-free Allocation of Indivisible Goods and Chores

Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2020/6 ◽

2020 ◽

Cited By ~ 3

Author(s):

Haris Aziz ◽

Simon Rey

Keyword(s):

Resource Allocation ◽

Polynomial Time ◽

Fair Allocation ◽

Indivisible Goods ◽

Preference Domain ◽

Polynomial Time Algorithms ◽

Multi Agent ◽

Additive Utilities ◽

Natural Classes ◽

Allocation Of Indivisible Items

We consider a multi-agent resource allocation setting in which an agent's utility may decrease or increase when an item is allocated. We take the group envy-freeness concept that is well-established in the literature and present stronger and relaxed versions that are especially suitable for the allocation of indivisible items. Of particular interest is a concept called group envy-freeness up to one item (GEF1). We then present a clear taxonomy of the fairness concepts. We study which fairness concepts guarantee the existence of a fair allocation under which preference domain. For two natural classes of additive utilities, we design polynomial-time algorithms to compute a GEF1 allocation. We also prove that checking whether a given allocation satisfies GEF1 is coNP-complete when there are either only goods, only chores or both.

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Fair Allocation of Indivisible Goods and Chores

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2019/8 ◽

2019 ◽

Cited By ~ 6

Author(s):

Haris Aziz ◽

Ioannis Caragiannis ◽

Ayumi Igarashi ◽

Toby Walsh

Keyword(s):

General Setting ◽

Task Assignment ◽

Fair Division ◽

Efficient Algorithms ◽

Fair Allocation ◽

Computational Results ◽

Indivisible Goods ◽

Fairness And Efficiency

We consider the problem of fairly dividing a set of items. Much of the fair division literature assumes that the items are ``goods'' i.e., they yield positive utility for the agents. There is also some work where the items are ``chores'' that yield negative utility for the agents. In this paper, we consider a more general scenario where an agent may have negative or positive utility for each item. This framework captures, e.g., fair task assignment, where agents can have both positive and negative utilities for each task. We show that whereas some of the positive axiomatic and computational results extend to this more general setting, others do not. We present several new and efficient algorithms for finding fair allocations in this general setting. We also point out several gaps in the literature regarding the existence of allocations satisfying certain fairness and efficiency properties and further study the complexity of computing such allocations.

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