11 research outputs found
Local Envy-Freeness in House Allocation Problems
International audienceWe study the fair division problem consisting in allocating one item per agent so as to avoid (or minimize) envy, in a setting where only agents connected in a given social network may experience envy. In a variant of the problem, agents themselves can be located on the network by the central authority. These problems turn out to be difficult even on very simple graph structures, but we identify several tractable cases. We further provide practical algorithms and experimental insights
Envy-freeness in house allocation problems
We consider the house allocation problem, where m houses are to be assigned to n agents so that each agent gets exactly one house. We present a polynomial-time algorithm that determines whether an envy-free assignment exists, and if so, computes one such assignment. We also show that an envy-free assignment exists with high probability if the number of houses exceeds the number of agents by a logarithmic factor
Fair Division through Information Withholding
Envy-freeness up to one good (EF1) is a well-studied fairness notion for
indivisible goods that addresses pairwise envy by the removal of at most one
good. In the worst case, each pair of agents might require the (hypothetical)
removal of a different good, resulting in a weak aggregate guarantee. We study
allocations that are nearly envy-free in aggregate, and define a novel fairness
notion based on information withholding. Under this notion, an agent can
withhold (or hide) some of the goods in its bundle and reveal the remaining
goods to the other agents. We observe that in practice, envy-freeness can be
achieved by withholding only a small number of goods overall. We show that
finding allocations that withhold an optimal number of goods is computationally
hard even for highly restricted classes of valuations. In contrast to the
worst-case results, our experiments on synthetic and real-world preference data
show that existing algorithms for finding EF1 allocations withhold
close-to-optimal number of goods.Comment: Full version of AAAI2020 paper. V2 has reviewers' comments
incorporated. V3 consists of updates to Section 7.
Fair Resource Sharing with Externailities
We study a fair resource sharing problem, where a set of resources are to be
shared among a set of agents. Each agent demands one resource and each resource
can serve a limited number of agents. An agent cares about what resource they
get as well as the externalities imposed by their mates, whom they share the
same resource with. Apparently, the strong notion of envy-freeness, where no
agent envies another for their resource or mates, cannot always be achieved and
we show that even to decide the existence of such a strongly envy-free
assignment is an intractable problem. Thus, a more interesting question is
whether (and in what situations) a relaxed notion of envy-freeness, the Pareto
envy-freeness, can be achieved: an agent i envies another agent j only when i
envies both the resource and the mates of j. In particular, we are interested
in a dorm assignment problem, where students are to be assigned to dorms with
the same capacity and they have dichotomous preference over their dorm-mates.
We show that when the capacity of the dorms is 2, a Pareto envy-free assignment
always exists and we present a polynomial-time algorithm to compute such an
assignment; nevertheless, the result fails to hold immediately when the
capacities increase to 3, in which case even Pareto envy-freeness cannot be
guaranteed. In addition to the existential results, we also investigate the
implications of envy-freeness on proportionality in our model and show that
envy-freeness in general implies approximations of proportionality
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