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On linear transformations of intersections


Kushnir, Alexey; Liu, Shuo (2017). On linear transformations of intersections. Working paper series / Department of Economics 255, University of Zurich.

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.

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.

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Economics
Working Paper Series > Department of Economics
Dewey Decimal Classification:330 Economics
JEL Classification:D82
Uncontrolled Keywords:Linear transformation, convex closed set, intersection, directional convexity, mechanism design, dominant-strategy implementation, Bayesian implementation
Language:English
Date:June 2017
Deposited On:06 Jun 2017 15:16
Last Modified:12 Sep 2017 08:52
Series Name:Working paper series / Department of Economics
Number of Pages:17
ISSN:1664-7041
Official URL:http://www.econ.uzh.ch/static/wp/econwp255.pdf
Related URLs:http://www.econ.uzh.ch/static/workingpapers.php

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