Demand-Flow of Agents with Gross-Substitute Valuations

TL;DR

This paper demonstrates that gross-substitute valuations ensure a downward demand-flow in markets with changing prices, a property that is stronger than previously understood and does not hold with complementarities.

Contribution

It proves that gross-substitute valuations imply a strong demand-flow condition in general price change scenarios, extending prior understanding of demand dynamics.

Findings

Demand always flows from higher to lower price-increase items.

The downward demand-flow property is equivalent to gross-substitute valuations.

The property does not hold when complementarities are present.

Abstract

We consider the class of valuations on indivisible items called gross-substitute (GS). This class was introduced by Kelso and Crawford (1982) and is widely used in studies of markets with indivisibilities. GS is a condition on the demand-flow in a specific scenario: some items become more expensive while other items retain their price. We prove that GS implies a much stronger condition, describing the demand-flow in the general scenario in which all prices may change. We prove that the demand of GS agents always flows (weakly) downwards, i.e, from items with higher price-increase to items with lower price-increase. We show that this property is equivalent to GS and is not true when there are complementarities.