Sequentially Optimal Pricing under Informational Robustness

A seller sells an object over time but is uncertain how the buyer learns their willingness-to-pay. We consider informational robustness under \textit{limited commitment}, where the seller offers a price \textit{each period} to maximize expected continuation profit against worst-case learning. Our formulation considers the worst case \textit{sequentially}. We characterize an essentially unique equilibrium under general conditions. We further show that, under mild conditions on the prior distribution, the equilibrium profit coincides exactly with the profit guaranteed by the equilibrium price path even under arbitrary (unrestricted) learning processes.