Vector mappings with diagonal images

Résumé

A diagonal image may be defined as a point in the image of agiven mapping, whose components are all equal. This paper investigates sufficient conditions for a set-valued mapping to have quasi-diagonal images(in an extended sense). More specifically, we shall show that anupper-hemicontinuous correspondence, with nonempty, compact andconvex values, applying the cartesian product of an arbitrarynumber of simplexes on the corresponding space, has aquasi-diagonal image. Two applications are provided in order to illustrate the usefulness of these points in econornic modelling.