The deficit on each trade in a Vickrey double auction is at least as large as the Walrasian price gap

Abstract

We prove that the deficit on each trade in a Vickrey double auction for a homogeneous good with multi-unit traders with multi-dimensional types is at least as large as the Walrasian price gap. We also show that as the number of traders grows large the aggregate deficit is bounded below by the ratio of the Walrasian price and the elasticity of excess supply at the Walrasian price.