Equilibrium selection: a geometric approach

TL;DR

This paper introduces a geometric method for equilibrium selection in economics, utilizing manifold projections and exponential maps, and establishes a link between zero curvature and equilibrium uniqueness.

Contribution

It presents a novel geometric framework for equilibrium selection and proves the equivalence between zero curvature and equilibrium uniqueness for multiple goods and consumers.

Findings

Equilibrium price selection can be modeled via geometric maps.

Zero curvature implies unique equilibrium in the studied economic model.

The approach extends previous results to multiple goods and consumers.

Abstract

In this paper we propose a geometric approach to the selection of the equi- librium price. After a perturbation of the parameters, the new price is selected thorough the composition of two maps: the projection on the linearization of the equilibrium man- ifold, a method that underlies econometric modeling, and the exponential map, that associates a tangent vector with a geodesic on the manifold. As a corollary of our main result, we prove the equivalence between zero curvature and uniqueness of equilibrium in the case of an arbitrary number of goods and two consumers, thus extending the previous result by [6].