Miglierina Enrico () (Department of Economics, University of Insubria, Italy)
Abstract
In this work we consider the critical points of a vector-valued function f, defined as in [17] and [23]. We study their stability in order to obtain a necessary condition for Paret efficiency. We point out, by an example, that the classical notions of stability (concerning a single point) are not suitable in the settings. We use a stability notion for sets to prove that the counterimage of a minimal point for f is stable.This result is based on the study of a dynamical system defined by a differential inclusion. In the vector case this inclusion plays the same role as gradient system in the scalar setting.
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