  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.
