Stability of Cournot duopoly games with isoelastic demands and quadratic costs

TL;DR

This paper analyzes the stability of Cournot duopoly games with isoelastic demand and quadratic costs, using symbolic methods to derive analytical results that show enlarged stability regions compared to linear costs.

Contribution

It introduces a symbolic computation approach to analyze duopoly stability with quadratic costs, extending classical results to more general cost structures.

Findings

Stability regions are larger with quadratic costs than with linear costs.

Symbolic methods yield analytical, rigorous stability conditions.

Results generalize classical stability findings in oligopoly models.

Abstract

In this discussion draft, we explore different duopoly games of players with quadratic costs, where the market is supposed to have the isoelastic demand. Different from the usual approaches based on numerical computations, the methods used in the present work are built on symbolic computations, which can produce analytical and rigorous results. Our investigations show that the stability regions are enlarged for the games considered in this work compared to their counterparts with linear costs, which generalizes the classical results of "F. M. Fisher. The stability of the Cournot oligopoly solution: The effects of speeds of adjustment and increasing marginal costs. The Review of Economic Studies, 28(2):125--135, 1961.".