University of Manchester Economics Discussion Paper No. EDP-0603
25 Pages Posted: 2 Mar 2006
Date Written: February 2006
The paper examines the problem of the existence of equilibrium for the stochastic analogue of the von Neumann-Gale model of economic growth. The mathematical framework of the model is a theory of set-valued random dynamical systems defined by positive stochastic operators with certain properties of convexity and homogeneity. Existence theorems for equilibria in such systems may be regarded as generalizations of the Perron-Frobenius theorem on eigenvalues and eigenvectors of positive matrices. The known results of this kind are obtained under rather restrictive assumptions. We show that these assumptions can be substantially relaxed if one allows for randomization. The main result of the paper is an existence theorem for randomized equilibria. Some special cases (models defined by positive matrices) are considered in which the existence of pure equilibria can be established.
Keywords: C61, C62, O41
JEL Classification: randomized von Neumann paths, sunspots
Suggested Citation: Suggested Citation
Evstigneev, Igor V. and Schenk-Hoppé, Klaus Reiner, Pure and Randomized Equilibria in the Stochastic Von Neumann-Gale Model (February 2006). University of Manchester Economics Discussion Paper No. EDP-0603. Available at SSRN: https://ssrn.com/abstract=887412 or http://dx.doi.org/10.2139/ssrn.887412