2,656 research outputs found
When Do Envy-Free Allocations Exist?
We consider a fair division setting in which indivisible items are to be
allocated among agents, where the agents have additive utilities and the
agents' utilities for individual items are independently sampled from a
distribution. Previous work has shown that an envy-free allocation is likely to
exist when but not when , and left open the
question of determining where the phase transition from non-existence to
existence occurs. We show that, surprisingly, there is in fact no universal
point of transition---instead, the transition is governed by the divisibility
relation between and . On the one hand, if is divisible by , an
envy-free allocation exists with high probability as long as . On the
other hand, if is not "almost" divisible by , an envy-free allocation is
unlikely to exist even when .Comment: Appears in the 33rd AAAI Conference on Artificial Intelligence
(AAAI), 201
Fair Division of a Graph
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 where the 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.Comment: 9 pages, long version of accepted IJCAI-17 pape
Democratic Fair Allocation of Indivisible Goods
We study the problem of fairly allocating indivisible goods to groups of
agents. Agents in the same group share the same set of goods even though they
may have different preferences. Previous work has focused on unanimous
fairness, in which all agents in each group must agree that their group's share
is fair. Under this strict requirement, fair allocations exist only for small
groups. We introduce the concept of democratic fairness, which aims to satisfy
a certain fraction of the agents in each group. This concept is better suited
to large groups such as cities or countries. We present protocols for
democratic fair allocation among two or more arbitrarily large groups of agents
with monotonic, additive, or binary valuations. For two groups with arbitrary
monotonic valuations, we give an efficient protocol that guarantees
envy-freeness up to one good for at least of the agents in each group,
and prove that the fraction is optimal. We also present other protocols
that make weaker fairness guarantees to more agents in each group, or to more
groups. Our protocols combine techniques from different fields, including
combinatorial game theory, cake cutting, and voting.Comment: Appears in the 27th International Joint Conference on Artificial
Intelligence and the 23rd European Conference on Artificial Intelligence
(IJCAI-ECAI), 201
For One and All: Individual and Group Fairness in the Allocation of Indivisible Goods
Fair allocation of indivisible goods is a well-explored problem.
Traditionally, research focused on individual fairness - are individual agents
satisfied with their allotted share? - and group fairness - are groups of
agents treated fairly? In this paper, we explore the coexistence of individual
envy-freeness (i-EF) and its group counterpart, group weighted envy-freeness
(g-WEF), in the allocation of indivisible goods. We propose several
polynomial-time algorithms that provably achieve i-EF and g-WEF simultaneously
in various degrees of approximation under three different conditions on the
agents' (i) when agents have identical additive valuation functions, i-EFX and
i-WEF1 can be achieved simultaneously; (ii) when agents within a group share a
common valuation function, an allocation satisfying both i-EF1 and g-WEF1
exists; and (iii) when agents' valuations for goods within a group differ, we
show that while maintaining i-EF1, we can achieve a 1/3-approximation to
ex-ante g-WEF1. Our results thus provide a first step towards connecting
individual and group fairness in the allocation of indivisible goods, in hopes
of its useful application to domains requiring the reconciliation of diversity
with individual demands.Comment: Appears in the 22nd International Conference on Autonomous Agents and
Multiagent Systems (AAMAS), 202
Developments in Multi-Agent Fair Allocation
Fairness is becoming an increasingly important concern when designing
markets, allocation procedures, and computer systems. I survey some recent
developments in the field of multi-agent fair allocation
Almost Group Envy-free Allocation of Indivisible Goods and Chores
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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