3 research outputs found
Group Envy Freeness and Group Pareto Efficiency in Fair Division with Indivisible Items
We study the fair division of items to agents supposing that agents can form
groups. We thus give natural generalizations of popular concepts such as
envy-freeness and Pareto efficiency to groups of fixed sizes. Group
envy-freeness requires that no group envies another group. Group Pareto
efficiency requires that no group can be made better off without another group
be made worse off. We study these new group properties from an axiomatic
viewpoint. We thus propose new fairness taxonomies that generalize existing
taxonomies. We further study near versions of these group properties as
allocations for some of them may not exist. We finally give three prices of
group fairness between group properties for three common social welfares (i.e.
utilitarian, egalitarian, and Nash).Comment: 14 pages, 2 figures, KI 201
Monotone and Online Fair Division
We study a new but simple model for online fair division in which indivisible
items arrive one-by-one and agents have monotone utilities over bundles of the
items. We consider axiomatic properties of mechanisms for this model such as
strategy-proofness, envy-freeness, and Pareto efficiency. We prove a number of
impossibility results that justify why we consider relaxations of the
properties, as well as why we consider restricted preference domains on which
good axiomatic properties can be achieved. We propose two mechanisms that have
good axiomatic fairness properties on restricted but common preference domains.Comment: 15 pages, 2 tables, KI 201
Online Learning Demands in Max-min Fairness
We describe mechanisms for the allocation of a scarce resource among multiple
users in a way that is efficient, fair, and strategy-proof, but when users do
not know their resource requirements. The mechanism is repeated for multiple
rounds and a user's requirements can change on each round. At the end of each
round, users provide feedback about the allocation they received, enabling the
mechanism to learn user preferences over time. Such situations are common in
the shared usage of a compute cluster among many users in an organisation,
where all teams may not precisely know the amount of resources needed to
execute their jobs. By understating their requirements, users will receive less
than they need and consequently not achieve their goals. By overstating them,
they may siphon away precious resources that could be useful to others in the
organisation. We formalise this task of online learning in fair division via
notions of efficiency, fairness, and strategy-proofness applicable to this
setting, and study this problem under three types of feedback: when the users'
observations are deterministic, when they are stochastic and follow a
parametric model, and when they are stochastic and nonparametric. We derive
mechanisms inspired by the classical max-min fairness procedure that achieve
these requisites, and quantify the extent to which they are achieved via
asymptotic rates. We corroborate these insights with an experimental evaluation
on synthetic problems and a web-serving task