Intertemporal Price Discrimination Via Randomized Pricing

In e-commerce, the price for a (durable) product could fluctuate very frequently. The undesirable but inevitable consequence is that consumers can be trained to time their purchases strategically. In this paper, we study randomized pricing, where the firm randomly varies prices over time, as an alternative dynamic pricing strategy. In particular, we consider a model where a monopolist sells a single product to a market with a constant stream of multiple market segments. The segments are heterogeneous in both their product valuations and patience levels. The firm pre-commits to a price distribution, and in each period, a price is randomly drawn from the chosen distribution. We characterize structural properties of optimal randomized pricing policies and show that under certain conditions that are also used in the literature, the optimal randomized pricing policy boils down to a two-point price distribution of a regular and discount price. Randomized pricing serves as an intertemporal price discrimination mechanism such that customers of higher valuations would buy immediately at the regular price upon arrival, and customers of lower valuations would wait for a promotion. Compared against the optimal cyclic deterministic pricing policy, which is optimal within the strategy space of all deterministic pricing policies, the optimal randomized pricing policy (weakly) dominates the optimal cyclic deterministic pricing policy if the valuation discrepancies among customers are large enough.