Pricing algorithms are computerized procedures a seller may use to adapt instantaneously its price to market conditions, including to prices quoted by its rivals. These algorithms are related to the extensive use of web-collectors which contribute in many industries to identifying the best price. In such settings, price competition operates between algorithms, no longer between executives of brick and mortar companies. In this context, the question is to know how implicit forms of collusion may arise between the sellers. This paper is aimed at discussing this conceptual issue in a price-setting homogeneous product oligopoly with decreasing returns to scale where algorithms implement matching policies. Using fixed point argument, we find a family of equilibrium prices encompassing Cournot and Pareto efficient solutions, if matching is allowed upward and downward. Dynamical stability is studied in the linear demand constant return case. When matching operates only for price undercutting, this family is extended up to a bottom value of the market price, close to the Walrasian price. Pricing algorithms may solve the Bertrand–Edgeworth paradox.

定价算法是卖方可以使用的计算机化程序，可即时将其价格调整为适应市场条件，包括其竞争对手报价的价格。这些算法与网络收集器的广泛使用有关，网络收集器在许多行业中为确定最佳价格做出了贡献。在这种情况下，价格竞争在算法之间进行，而不再在实体公司的高管之间进行。在这种情况下，问题是要知道在卖方之间如何可能会出现隐含的串通形式。本文旨在讨论价格设定同质产品寡头垄断中的这一概念性问题，随着算法实现匹配策略，规模收益递减。利用定点论证，我们找到了一个包含古诺和帕累托有效解的均衡价格族，如果允许向上和向下匹配。研究了线性需求恒定收益情况下的动力稳定性。当匹配仅用于降价操作时，此系列将扩展到市场价格的底值，接近Walrasian价格。定价算法可以解决Bertrand–Edgeworth悖论。