AI 中文总结
本文针对伯特兰双头垄断中异步设定价格的Q-learning算法，通过大量数值实验探究异步性对算法合谋的影响，发现异步性会阻碍合谋，相关结果对算法定价监管具有意义。
AI 中文摘要
本文研究智能体更新的异步性对算法合谋产生的影响。我们提出了一种算法合谋的连续时间模型，其中两家企业使用Q-learning算法在伯特兰双头垄断中异步设定价格，企业的价格更新由泊松时钟决定的时间触发。通过控制智能体异步性的程度，我们针对三种算法规格开展了大量数值实验，以探究算法合谋的产生情况。合谋强度通过标准合谋指数以及自动检测奖惩机制来衡量，具体做法是记录大量算法对单方降价的反应，并将其与未训练算法的反应进行对比。我们的研究结果表明，异步性会阻碍合谋，尤其是在算法为无状态时；当算法以竞争对手的先前价格为条件时，算法合谋对异步性的敏感性会因算法可获取的信息类型不同而有所差异。我们还讨论了这些结果对算法定价监管的意义。
英文摘要
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.
