4 research outputs found
Robust Market Equilibria with Uncertain Preferences
The problem of allocating scarce items to individuals is an important
practical question in market design. An increasingly popular set of mechanisms
for this task uses the concept of market equilibrium: individuals report their
preferences, have a budget of real or fake currency, and a set of prices for
items and allocations is computed that sets demand equal to supply. An
important real world issue with such mechanisms is that individual valuations
are often only imperfectly known. In this paper, we show how concepts from
classical market equilibrium can be extended to reflect such uncertainty. We
show that in linear, divisible Fisher markets a robust market equilibrium (RME)
always exists; this also holds in settings where buyers may retain unspent
money. We provide theoretical analysis of the allocative properties of RME in
terms of envy and regret. Though RME are hard to compute for general
uncertainty sets, we consider some natural and tractable uncertainty sets which
lead to well behaved formulations of the problem that can be solved via modern
convex programming methods. Finally, we show that very mild uncertainty about
valuations can cause RME allocations to outperform those which take estimates
as having no underlying uncertainty.Comment: Extended preprint of an article accepted to AAAI-20. Contains
supplementary material as appendices. Due to figures, this manuscript is best
printed in colo
Statistical Inference for Fisher Market Equilibrium
Statistical inference under market equilibrium effects has attracted
increasing attention recently. In this paper we focus on the specific case of
linear Fisher markets. They have been widely use in fair resource allocation of
food/blood donations and budget management in large-scale Internet ad auctions.
In resource allocation, it is crucial to quantify the variability of the
resource received by the agents (such as blood banks and food banks) in
addition to fairness and efficiency properties of the systems. For ad auction
markets, it is important to establish statistical properties of the platform's
revenues in addition to their expected values. To this end, we propose a
statistical framework based on the concept of infinite-dimensional Fisher
markets. In our framework, we observe a market formed by a finite number of
items sampled from an underlying distribution (the "observed market") and aim
to infer several important equilibrium quantities of the underlying long-run
market. These equilibrium quantities include individual utilities, social
welfare, and pacing multipliers. Through the lens of sample average
approximation (SSA), we derive a collection of statistical results and show
that the observed market provides useful statistical information of the
long-run market. In other words, the equilibrium quantities of the observed
market converge to the true ones of the long-run market with strong statistical
guarantees. These include consistency, finite sample bounds, asymptotics, and
confidence. As an extension, we discuss revenue inference in quasilinear Fisher
markets