Computing Equilibria of Semi-algebraic Economies Using Triangular Decomposition and Real Solution Classification

TL;DR

This paper introduces a comprehensive algebraic method using triangular decomposition and real solution classification to determine multiple equilibria in semi-algebraic economic models.

Contribution

It presents a novel, complete approach for identifying equilibrium multiplicities in semi-algebraic economies, leveraging advanced algebraic computation tools.

Findings

Successfully applied to example models demonstrating effectiveness

Accurately identifies the number of equilibria

Provides a systematic algebraic framework for economic analysis

Abstract

In this paper, we are concerned with the problem of determining the existence of multiple equilibria in economic models. We propose a general and complete approach for identifying multiplicities of equilibria in semi-algebraic economies, which may be expressed as semi-algebraic systems. The approach is based on triangular decomposition and real solution classification, two powerful tools of algebraic computation. Its effectiveness is illustrated by two examples of application.