Learning to Compete under Unknown Demand In many markets, firms must set prices while competing with others and learning demand from limited data, yet they rarely know how demand responds to prices or how competitors will react. Most existing models assume full knowledge of demand or access to competitors’ information, which limits practical relevance. In “LEGO: Optimal Online Learning Under Sequential Price Competition,” S. Li, C. Shi, and S. Mehrotra study a dynamic pricing problem in which multiple sellers repeatedly compete while observing only their own demand. The authors propose a decentralized learning algorithm that combines exploration with gradient-based price updates and does not require information sharing among competitors. They show that each seller’s revenue loss grows at the minimal rate and that prices converge to the Nash equilibrium over time. Their results identify uncertainty in individual price sensitivity as the main challenge and provide a practical framework for data-driven pricing under competition.
Li et al. (Wed,) studied this question.