Intertemporal Price Discrimination via Randomized Promotions.

This article investigates randomized promotions as an alternative dynamic pricing strategy for a monopolist selling a single product to sequentially arriving customers segmented by heterogeneous valuations and patience levels. It characterizes the optimal randomized pricing policy as a two-point price distribution that enables intertemporal price discrimination: high-valuation customers purchase immediately at a high price, while low-valuation customers wait for random discounts. Compared to optimal static and cyclic deterministic pricing policies, randomized pricing yields higher profits when low-valuation customers are sufficiently patient and valuation differences are large, though neither randomized nor cyclic pricing universally dominates the other. Extensions include models with myopic customers, Markovian pricing policies allowing intertemporal price correlation, and multiple customer segments, with results showing that Markovian pricing can further increase profitability and that the two-point distribution remains optimal under certain conditions. The findings suggest firms may benefit from deliberately randomizing promotions to mitigate strategic waiting behavior and improve profitability, especially in markets with diverse customer valuations and patience.