Algorithmic collusion under asynchronous price updating

2026-08-02

AI Summary

This study investigates the impact of asynchronous price updates on algorithmic collusion. Building a continuous-time duopoly model in which firms asynchronously perform Q-learning driven by Poisson processes, the authors conduct large-scale numerical experiments to systematically quantify how the degree of asynchronicity suppresses collusive behavior. They innovatively introduce a collusion index and a behavioral response comparison framework, complemented by a novel method capable of automatically identifying punishment-and-reward mechanisms to assess collusion intensity. The results demonstrate that asynchronicity significantly weakens collusion, particularly in stateless algorithms; moreover, when algorithms can observe rivals’ historical prices, the sensitivity of collusion to asynchronicity hinges on the type of information acquired. This work provides the first systematic evidence of the critical role of asynchronous updating in mitigating tacit algorithmic collusion.

Abstract

This paper investigates the effect of asynchrony in agents' updates in the emergence of algorithmic collusion. We present a continuous-time model for algorithmic collusion in which two firms use $Q$-learning algorithms to set prices asynchronously in a Bertrand duopoly. The firms update their prices at times dictated by a Poisson clock. By controlling the extent of agents' asynchrony, we run extensive numerical experiments with three specifications of the algorithm to investigate the emergence of algorithmic collusion. The strength of collusion is measured by a standard collusion index, as well as by automatically detecting the reward-punishment schemes. This is done by recording a large number of algorithms' reactions to unilateral price cuts and comparing them with the reactions of untrained algorithms. Our findings indicate that asynchrony hampers collusion, especially when the algorithms are stateless. When they condition on their competitor's previous prices, the sensitivity of algorithmic collusion to asynchrony varies depending on the type of information they have access to. The implications of these results for the regulation of algorithmic pricing are discussed.

Problem

• algorithmic collusion
• asynchronous updating
• Q-learning
• Bertrand duopoly
• price setting

Innovation

• algorithmic collusion
• asynchronous updating
• Q-learning
• Bertrand duopoly
• reward-punishment schemes