11 research outputs found
Fairly Allocating Many Goods with Few Queries
We investigate the query complexity of the fair allocation of indivisible
goods. For two agents with arbitrary monotonic valuations, we design an
algorithm that computes an allocation satisfying envy-freeness up to one good
(EF1), a relaxation of envy-freeness, using a logarithmic number of queries. We
show that the logarithmic query complexity bound also holds for three agents
with additive valuations. These results suggest that it is possible to fairly
allocate goods in practice even when the number of goods is extremely large. By
contrast, we prove that computing an allocation satisfying envy-freeness and
another of its relaxations, envy-freeness up to any good (EFX), requires a
linear number of queries even when there are only two agents with identical
additive valuations
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
The Convergence of Finite-Averaging of AIMD for Distributed Heterogeneous Resource Allocations
In several social choice problems, agents collectively make decisions over
the allocation of multiple divisible and heterogeneous resources with capacity
constraints to maximize utilitarian social welfare. The agents are constrained
through computational or communication resources or privacy considerations. In
this paper, we analyze the convergence of a recently proposed distributed
solution that allocates such resources to agents with minimal communication. It
is based on the randomized additive-increase and multiplicative-decrease (AIMD)
algorithm. The agents are not required to exchange information with each other,
but little with a central agent that keeps track of the aggregate resource
allocated at a time. We formulate the time-averaged allocations over finite
window size and model the system as a Markov chain with place-dependent
probabilities. Furthermore, we show that the time-averaged allocations vector
converges to a unique invariant measure, and also, the ergodic property holds
Fairly allocating many goods with few queries
We investigate the query complexity of the fair allocation of indivisible goods. For two agents with arbitrary monotonic valuations, we design an algorithm that computes an allocation satisfying envy-freeness up to one good (EF1), a relaxation of envy-freeness, using a logarithmic number of queries. We show that the logarithmic query complexity bound also holds for three agents with additive valuations. These results suggest that it is possible to fairly allocate goods in practice even when the number of goods is extremely large. By contrast, we prove that computing an allocation satisfying envyfreeness and another of its relaxations, envy-freeness up to any good (EFX), requires a linear number of queries even when there are only two agents with identical additive valuations
Fairly allocating many goods with few queries
We investigate the query complexity of the fair allocation of indivisible goods. For two agents with arbitrary monotonic valuations, we design an algorithm that computes an allocation satisfying envy-freeness up to one good (EF1), a relaxation of envy-freeness, using a logarithmic number of queries. We show that the logarithmic query complexity bound also holds for three agents with additive valuations. These results suggest that it is possible to fairly allocate goods in practice even when the number of goods is extremely large. By contrast, we prove that computing an allocation satisfying envyfreeness and another of its relaxations, envy-freeness up to any good (EFX), requires a linear number of queries even when there are only two agents with identical additive valuations
Efficient Fair Division with Minimal Sharing
A collection of objects, some of which are good and some are bad, is to be
divided fairly among agents with different tastes, modeled by additive
utility-functions. If the objects cannot be shared, so that each of them must
be entirely allocated to a single agent, then a fair division may not exist.
What is the smallest number of objects that must be shared between two or more
agents in order to attain a fair and efficient division? We focus on
Pareto-optimal, envy-free and/or proportional allocations. We show that, for a
generic instance of the problem -- all instances except of a zero-measure set
of degenerate problems -- a fair Pareto-optimal division with the smallest
possible number of shared objects can be found in polynomial time, assuming
that the number of agents is fixed. The problem becomes computationally hard
for degenerate instances, where agents' valuations are aligned for many
objects.Comment: Add experiments with Spliddit.org dat
The Price of Connectivity in Fair Division
We study the allocation of indivisible goods that form an undirected graph
and quantify the loss of fairness when we impose a constraint that each agent
must receive a connected subgraph. Our focus is on well-studied fairness
notions including envy-freeness and maximin share fairness. We introduce the
price of connectivity to capture the largest gap between the graph-specific and
the unconstrained maximin share, and derive bounds on this quantity which are
tight for large classes of graphs in the case of two agents and for paths and
stars in the general case. For instance, with two agents we show that for
biconnected graphs it is possible to obtain at least of the maximin share
with connected allocations, while for the remaining graphs the guarantee is at
most . In addition, we determine the optimal relaxation of envy-freeness
that can be obtained with each graph for two agents, and characterize the set
of trees and complete bipartite graphs that always admit an allocation
satisfying envy-freeness up to one good (EF1) for three agents. Our work
demonstrates several applications of graph-theoretic tools and concepts to fair
division problems