Colluding price algorithms


In an increasing number of marketplaces, selling prices are determined by self-learning algorithms. Although the advantages of this technological innovation have frequently been praised, recently several economists and lawmakers have expressed their concerns about a potential danger of these algorithms. Concretely, one is concerned about the possibility that these algorithms will learn - without mutual communication - to collude instead of compete with each other.

Legal experts agree that this form of collusion is disadvantageous for consumer welfare but most likely not against anti-trust law, and that therefore the existing legislation has to be modified. However, several economists have recently argued that it is very difficult, if not impossible, for algorithms to learn to collude without mutual communication; and if they would need some form of communication to agree on collusion, then this would already be illegal under existing anti-trust law. Hence, there is a great urgency to determine whether or not algorithms are capable of learning to collude in realistic market scenarios, without mutual communication.

In this research project we will show that this is indeed possible. We will design such an algorithm and prove that selling prices will almost surely converge to supra-competitive prices when the algorithm plays against copies of itself. Not all players in the market have to use the same algorithm, and no limit is imposed on the number of players or the number of feasible actions (prices). We allow for very general demand models, including choice models that account for product heterogeneity. We will provide a theoretical analysis to show that the algorithm is asymptotically optimal in a precisely defined sense; in addition we will demonstrate its practical performance in existing simulation environments for dynamic pricing. The main expected outcome of this research project is a communication-free pricing algorithm that learns to collude in realistic market scenarios.





Dr. A.V. den Boer

Verbonden aan

Universiteit van Amsterdam, Faculteit der Natuurwetenschappen, Wiskunde en Informatica, Korteweg-de Vries Instituut voor de Wiskunde


01/03/2019 tot 28/02/2023