Correspondences

  • Charalambos D. Aliprantis
  • Kim C. Border

Abstract

A correspondence is a set-valued function. That is, a correspondence associates to each point in one set a set of points in another set. As such, it can be viewed simply as a subset of the Cartesian product of the two sets. It may seem a bit silly to dedicate two chapters to such a topic, but correspondences arise naturally in many applications. For instance, the budget correspondence in economic theory associates the set of affordable consumption bundles to each price-income combination; the excess demand correspondence is a useful tool in studying economic equilibria; and the best-reply correspondence is the key to analyzing noncooperative games. The theory of “differential inclusions” deals with set-valued differential equations and plays an important role in control theory.

Keywords

Hull Topo Verse Stam 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Charalambos D. Aliprantis
    • 1
  • Kim C. Border
    • 2
  1. 1.Department of EconomicsPurdue UniversityWest LafayetteUSA
  2. 2.Division of the Humanities and Social Sciences 228-77California Institute of TechnologyPasadenaUSA

Personalised recommendations