Algorithmic Collusion in Assortment Games

This paper contributes to the ongoing debate on the plausibility of tacit collusion between sellers in algorithmic marketplaces, which can be very detrimental to customers and social welfare. We study a broad class of assortment decisions routinely made by sellers on online platforms, including which set of products is offered to customers, at what price, and how are they displayed. In this context, algorithmic decision-support tools are extensively studied in the operations literature and widely adopted in practice. We propose simple notions of collusive outcomes to describe an "optimal form" of collusion between sellers under full information. While computing such collusive outcomes is NP-hard, we develop a polynomial-time approximation scheme, showcasing the computational tractability afforded by our solution concept. Our main contribution is to establish that collusive outcomes can be tacitly and near-optimally reached under very limited prior market information. Surprisingly, we show that a simple variant of epsilon-greedy -- a commonly used class of learn-and-earn algorithms -- is able to dynamically learn a collusive outcome without any form of explicit communication that is prohibited by antitrust laws. This algorithm asymptotically attains a collusive outcome with a worst-case expected regret of O(T^{2/3}\log T) over T periods against the full-information benchmark. The collusive algorithms we construct do not involve any form of explicit communication between sellers, which might have important ramifications on the regulators' ability to enforce competition laws and antitrust policies.