Stochastic Equilibria in Von Neumann-Gale Dynamical Systems

Abstract

The paper examines a class of random dynamical systems related to the classical von Neumann and Gale models of economic dynamics. Such systems are defined in terms of multivalued operators in spaces of random vectors, possessing certain properties of convexity and homogeneity. We establish a general existence theorem for equilibrium, which holds under conditions analogous to the standard deterministic ones. Our results answer questions that remained open for more than three decades.

Keywords: Random dynamical systems, convex multivalued operators, von Neumann-Gale model, rapid paths, convex duality, stochastic equilibrium

JEL Classification: C61, C62, O41