Cournot duopoly games with isoelastic demands and diseconomies of scale

TL;DR

This paper analyzes five duopoly models with isoelastic demand and decreasing returns to scale, revealing how diseconomies of scale can enhance stability in market competition.

Contribution

It introduces new duopoly models incorporating isoelastic demand and diseconomies of scale, analyzing their equilibria and stability through symbolic computation.

Findings

Diseconomies of scale improve stability in duopoly games.

Equilibria are characterized and analyzed using nonlinear difference equations.

Stability effects are consistent with previous findings for linear demand models.

Abstract

In this discussion draft, we investigate five different models of duopoly games, where the market is assumed to have an isoelastic demand function. Moreover, quadratic cost functions reflecting decreasing returns to scale are considered. The games in this draft are formulated with systems of two nonlinear difference equations. Existing equilibria and their local stability are analyzed by symbolic computations. In the model where a gradiently adjusting player and a rational (or a boundedly rational) player compete with each other, diseconomies of scale are proved to have an effect of stability enhancement, which is consistent with the similar results found by Fisher for homogeneous oligopolies with linear demand functions.