On the Oscillations in Cournot Games with Best Response Strategies

TL;DR

This paper investigates the dynamic oscillations in Cournot oligopoly models with best response strategies, establishing conditions for convergence and oscillation, and providing algorithms to identify oscillatory behaviors.

Contribution

It is the first to analyze periodic oscillations in Cournot models with best response updates and offers algorithms to detect two-period oscillations.

Findings

Oscillations exist under certain conditions in Cournot models.

Best response strategies can lead to convergence or two-period oscillations.

Algorithms are provided to find all two-period oscillations efficiently.

Abstract

In this paper, we consider the dynamic oscillation in the Cournot oligopoly model, which involves multiple firms producing homogeneous products. To explore the oscillation under the updates of best response strategies, we focus on the linear price functions. In this setting, we establish the existence of oscillations. In particular, we show that for the scenario of different costs among firms, the best response converges to either a unique equilibrium or a two-period oscillation. We further characterize the oscillations and propose linear-time algorithms for finding all types of two-period oscillations. To the best of our knowledge, our work is the first step toward fully analyzing the periodic oscillation in the Cournot oligopoly model.