Robust Market Equilibria with Uncertain Preferences

TL;DR

This paper extends classical market equilibrium concepts to uncertain preferences, proving the existence of robust market equilibria in linear Fisher markets and analyzing their properties and computational aspects.

Contribution

It introduces the concept of robust market equilibrium (RME) under preference uncertainty, proving existence in linear Fisher markets and exploring tractable computation methods.

Findings

RME always exists in linear Fisher markets with uncertain preferences.

RME allocations can outperform deterministic estimates under mild uncertainty.

Certain natural uncertainty sets lead to convex optimization formulations.

Abstract

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.