On Invariance and Periodicity Properties in Set-Valued Processes

Abstract

Set-valued mappings (correspondences) arise in economic theory in quite different fields. They were used for instance by John v. Neumann in order to investigate the equilibria in input-output models and they are a main instrument of production theory since the early fifties. More recently correspondences are used to describe the dynamic behaviour of an economy [see e.g. Champsaur/Drèze/Henry; Cherene], In these cases a set-valued process is considered, which determines (in the discrete case) the set of all possible states at time t + 1 given the state at time t; in the continuous case the set valued process is given by a set-valued differential equation (Set-valued differential equations or generalized dynamical systems are described in Roxin.