# Stability analysis of heterogeneous oligopoly games of increasing players: A computational approach

## TL;DR

This paper studies how market stability changes as more diverse companies join an industry, using mathematical models and simulations.

## Contribution

The paper introduces a computational approach to analyze stability in heterogeneous oligopoly games with increasing players.

## Key findings

- Stability regions grow larger as more heterogeneous firms are added.
- Complex dynamics like chaos emerge when equilibrium is lost.
- Dynamics are more complex with distinct cost parameters.

## Abstract

In this paper, we study an oligopolistic market endowed with an isoelastic demand function and a quadratic cost function, where heterogeneous firms coexist and produce the same product. We create new games by adding additional heterogeneous firms one after the other, and we examine the relative size of the stability region as the number of heterogeneous firms increases. For each model studied, we use the cylindrical algebraic decomposition method to analytically investigate the conditions for the local stability of the Cournot–Nash equilibrium. We find that the stability regions become larger as the number of heterogeneous firms involved increases. We also perform numerical simulations to investigate complex dynamics, such as periodic orbits and chaos, when the equilibrium loses its stability. Furthermore, we investigate the case of distinct cost parameters through numerical simulations and find that the dynamics seem more complicated than the case of identical cost parameters.