Stability analysis of heterogeneous oligopoly games of increasing players with quadratic costs

TL;DR

This paper analyzes the stability of heterogeneous oligopoly games with increasing players and quadratic costs under isoelastic demand, showing that stability regions expand as more firms participate.

Contribution

It provides analytical conditions for local stability and demonstrates how stability regions grow with the number of firms in oligopoly models.

Findings

Stability regions increase with more firms.

Necessary and sufficient conditions for local stability derived.

Analytical proofs for stability expansion as players increase.

Abstract

In this discussion draft, we explore heterogeneous oligopoly games of increasing players with quadratic costs, where the market is supposed to have the isoelastic demand. For each of the models considered in this draft, we analytically investigate the necessary and sufficient condition of the local stability of its positive equilibrium. Furthermore, we rigorously prove that the stability regions are enlarged as the number of involved firms is increasing.