On Linear Transformations of Intersections

17 Pages Posted: 18 Apr 2017 Last revised: 6 Sep 2017

See all articles by Alexey I. Kushnir

Alexey I. Kushnir

Carnegie Mellon University - David A. Tepper School of Business

Shuo Liu

University of Zurich, Department of Economics, Students

Date Written: September 6, 2017

Abstract

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

Kushnir, Alexey I. and Liu, Shuo, On Linear Transformations of Intersections (September 6, 2017). Available at SSRN: https://ssrn.com/abstract=2953459 or http://dx.doi.org/10.2139/ssrn.2953459

Alexey I. Kushnir

Carnegie Mellon University - David A. Tepper School of Business ( email )

5000 Forbes Avenue
Pittsburgh, PA 15213-3890
United States

Shuo Liu (Contact Author)

University of Zurich, Department of Economics, Students ( email )

Zurich
Switzerland

HOME PAGE: http://www.econ.uzh.ch/en/people/graduatestudents/sliu.html

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