On Linear Transformations of Intersections
17 Pages Posted: 18 Apr 2017 Last revised: 6 Sep 2017
Date Written: September 6, 2017
For any linear transformation and two convex closed sets, we provide necessary and sufficient conditions for when the transformation of the intersection of the sets coincides with the intersection of their images. We also identify analogous conditions for non-convex sets, general transformations, and multiple sets. We demonstrate the usefulness of our results via an application to the economics literature of mechanism design.
Keywords: linear transformation, convex closed set, intersection, directional convexity, mechanism design, dominant-strategy implementation, Bayesian implementation
JEL Classification: D82
Suggested Citation: Suggested Citation