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Contribution Details

Type Working Paper
Scope Discipline-based scholarship
Title On linear transformations of intersections
Organization Unit
  • Alexey Kushnir
  • Shuo Liu
  • English
Institution University of Zurich
Series Name Working paper series / Department of Economics
Number 255
ISSN 1664-7041
Number of Pages 17
Date 2017
Abstract Text 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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Keywords Linear transformation, convex closed set, intersection, directional convexity, mechanism design, dominant-strategy implementation, Bayesian implementation, Konvexe Optimierung, Bayes-Verfahren, Stochastische Dominanz, Mechanismus-Design-Theorie