No Algorithmic Collusion in Two-Player Blindfolded Game with Thompson Sampling

Algorithmic collusion refers to the market phenomenon that when two or more competing parties use algorithms to assist decision-making, over time it may unintentionally lead to collusion instead of the typical Nash equilibrium. For example, consider two firms setting prices for their products, which are competing for customers. In the classic Bertrand competition, when the demand functions (how the market demand for either product depends on the prices of itself and the competitor) for both products are common knowledge, the firms may charge $10 in the (symmetric) Nash equilibrium. On the other hand, when the demand functions are unknown initially, the two firms may deploy reinforcement learning algorithms to learn the demand functions and maximize profits simultaneously. Algorithmic collusion emerges when the long-term outcome of the algorithms is an equilibrium in which both firms charge more than $10 for the products. It has been shown in the recent literature that algorithmic collusion is possible in theoretical and experimental settings [8, 15, 26].