Homotopies and the Instability of Economic Equilibria

Resumen

Homotopy theory has been sporadically applied to economic theory mainly in order to simplify the aggregation of preferences among agents (decision makers) in social choice and to design stable algorithms in computable general equilibrium models. These applications, while dealing with relevant issues, do not consider explicitly the influence of information asymmetries on the behaviour of agents, which constitutes a leading argument in current economic theory. The present paper aims to fill the existing gap and illustrate the main consequences derived from applying homotopy theory to an economic system where agents are asymmetrically informed. Indeed, we show that, when information asymmetries among agents are explicitly considered, a homotopic approach can be used as a destabilizing device in economic equilibrium theory. We use homotopy techniques to illustrate how the information sets determining the choices of agents can be modified to induce any a priori assigned economic equilibrium. More precisely, we investigate the conditions under which a homotopy can be defined such that a predetermined choice is imposed on an economic agent. In this way, choices and, consequently, equilibria are proved to be perfectly manipulable when such conditions apply. Besides its already important economic applications, our model displays immediate extensions in management and decision theory. © 2010 by Nova Science Publishers, Inc. All rights reserved.