62 research outputs found
Asymptotic Existence of Proportionally Fair Allocations
Fair division has long been an important problem in the economics literature.
In this note, we consider the existence of proportionally fair allocations of
indivisible goods, i.e., allocations of indivisible goods in which every agent
gets at least her proportionally fair share according to her own utility
function. We show that when utilities are additive and utilities for individual
goods are drawn independently at random from a distribution, proportionally
fair allocations exist with high probability if the number of goods is a
multiple of the number of agents or if the number of goods grows asymptotically
faster than the number of agents
Approximate Maximin Shares for Groups of Agents
We investigate the problem of fairly allocating indivisible goods among
interested agents using the concept of maximin share. Procaccia and Wang showed
that while an allocation that gives every agent at least her maximin share does
not necessarily exist, one that gives every agent at least of her share
always does. In this paper, we consider the more general setting where we
allocate the goods to groups of agents. The agents in each group share the same
set of goods even though they may have conflicting preferences. For two groups,
we characterize the cardinality of the groups for which a constant factor
approximation of the maximin share is possible regardless of the number of
goods. We also show settings where an approximation is possible or impossible
when there are several groups.Comment: To appear in the 10th International Symposium on Algorithmic Game
Theory (SAGT), 201
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
Computing an Approximately Optimal Agreeable Set of Items
We study the problem of finding a small subset of items that is
\emph{agreeable} to all agents, meaning that all agents value the subset at
least as much as its complement. Previous work has shown worst-case bounds,
over all instances with a given number of agents and items, on the number of
items that may need to be included in such a subset. Our goal in this paper is
to efficiently compute an agreeable subset whose size approximates the size of
the smallest agreeable subset for a given instance. We consider three
well-known models for representing the preferences of the agents: ordinal
preferences on single items, the value oracle model, and additive utilities. In
each of these models, we establish virtually tight bounds on the approximation
ratio that can be obtained by algorithms running in polynomial time.Comment: A preliminary version appeared in Proceedings of the 26th
International Joint Conference on Artificial Intelligence (IJCAI), 201
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
Weighted Fair Division with Matroid-Rank Valuations: Monotonicity and Strategyproofness
We study the problem of fairly allocating indivisible goods to agents with
weights corresponding to their entitlements. Previous work has shown that, when
agents have binary additive valuations, the maximum weighted Nash welfare rule
is resource-, population-, and weight-monotone, satisfies
group-strategyproofness, and can be implemented in polynomial time. We
generalize these results to the class of weighted additive welfarist rules with
concave functions and agents with matroid-rank (also known as binary
submodular) valuations.Comment: Appears in the 16th International Symposium on Algorithmic Game
Theory (SAGT), 202
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