Econ Papers Daily / 期刊论文
算法定价中的共谋趋同
Convergence to collusion in algorithmic pricing
摘要
Artificial intelligence algorithms are increasingly used by firms to set prices. Previous research shows that they can learn to collude, but how quickly and reliably they can do so has remained an open question. I study average-reward soft actor-critic algorithms that set continuous prices in the workhorse environment of this literature: a repeated Bertrand duopoly with symmetric firms, deterministic logit demand, and constant marginal costs, where agents observe only market prices and their own profits. The algorithms can converge to a collusive outcome within 50,000 periods, and in 36% of simulations learned punishments make one-period deviations unprofitable, so that high prices are mutual best responses. Successful simulations show cooperative behaviour supported by reward-punishment schemes that discourage deviations. When high prices are not supported by punishments, profitable deviations are typically on the order of hundredths of a percent.
中文摘要
人工智能算法正越来越多地被企业用于定价。既有研究表明，这些算法能够学会合谋，但其实现合谋的速度与可靠性仍是一个悬而未决的问题。本文研究平均奖励软演员-评论家算法，该算法在本文献的经典环境中设定连续价格：一个对称企业的重复伯特兰双寡头模型，具有确定性logit需求和不变边际成本，其中智能体仅能观察到市场价格和自身利润。这些算法能够在50,000个周期内收敛至合谋结果，并且在36%的模拟中，学到的惩罚机制使得单期偏离无利可图，从而高价成为相互最优反应。成功的模拟显示出由奖励-惩罚机制所支持的合作行为，该机制抑制了偏离。当高价未得到惩罚机制支持时，有利可图的偏离通常仅为百分之几的数量级。