Optimal allocation of an opaque product with consumer learning

We consider a firm offering an opaque good over one selling season, that is, a product whose full characteristics are only revealed after the consumer completes the transaction. In our model, the consumer can choose between buying either of two transparent goods offered on the market at given high- and low-price, respectively, or paying a price in between to purchase the firm’s opaque good. Given that, over time, consumers learn the firm’s allocation policy of high- and low-quality product via opaque selling, the seller’s objective is to determine the optimal sequence that maximizes its profit over the selling season. We characterize the unique optimal allocation sequence for any parameter constellation.