Demand-Flow of Agents with Gross-Substitute Valuations
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.
Keywords
Cite
@article{arxiv.1607.01989,
title = {Demand-Flow of Agents with Gross-Substitute Valuations},
author = {Erel Segal-Halevi and Avinatan Hassidim and Yonatan Aumann},
journal= {arXiv preprint arXiv:1607.01989},
year = {2016}
}
Comments
7 pages. Improved examples and added missing proofs