We show that if they are allowed enough time to complete the learning, Q-learning algorithms can learn to collude in an environment with imperfect monitoring adapted from Green and Porter (1984), without having been instructed to do so, and without communicating with one another. Collusion is sustained by punishments that take the form of “price wars” triggered by the observation of low prices. The punishments have a finite duration, being harsher initially and then gradually fading away. Such punishments are triggered both by deviations and by adverse demand shocks.

中文翻译：

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算法共谋与不完善的监控

我们表明，如果允许他们有足够的时间来完成学习，Q-learning 算法可以学习在 Green 和 Porter (1984) 改编的监控不完善的环境中串通，而无需被指示这样做，也无需与他人交流其他。以观察到低价引发的“价格战”形式的惩罚来维持共谋。惩罚的持续时间是有限的，最初是严厉的，然后逐渐消失。这种惩罚是由偏差和不利的需求冲击引发的。