Equilibria and their stability in an asymmetric duopoly model of Kopel

TL;DR

This paper analyzes the equilibria and their stability in an asymmetric duopoly model of Kopel, using symbolic computation tools to identify conditions for multiple equilibria and their stability under different strategic assumptions.

Contribution

It provides the first rigorous conditions for the existence of multiple positive equilibria in Kopel's asymmetric duopoly model, considering best response and adaptive expectations.

Findings

Conditions for multiple equilibria are established.

Existence of positive equilibria depends on specific model parameters.

Stability criteria are derived for different strategic behaviors.

Abstract

In this paper, we investigate the equilibria and their stability in an asymmetric duopoly model of Kopel by using several tools based on symbolic computations. We explore the possible positions of the equilibria in Kopel's model. We discuss the possibility of the existence of multiple positive equilibria and establish a necessary and sufficient condition for a given number of equilibria to exist. Furthermore, if the two duopolists adopt the best response reactions or homogeneous adaptive expectations, we establish rigorous conditions for the existence of distinct numbers of positive equilibria for the first time.