Optimal Selling Scheme for Heterogeneous Consumers with Uncertain Valuations

In this paper, we investigate the optimal selling scheme for a capacity-constrained seller who faces both aggregate demand and individual valuation uncertainties. As each consumer privately observes an initial estimate prior to the transactions and an updated information post-purchase, the problem exhibits the sequential screening feature and return policy emerges as part of the optimal selling scheme. We show that the optimal selling scheme nicely resembles the classical multi-unit auction design, and the product is returned too often compared to the efficient scenario. Furthermore, even though the post-purchase information update is privately observed by the individual consumers, the seller does not give away additional surplus to the consumers. Our general framework can accommodate various heterogeneities and uncertainties regarding hassle costs, shipping costs, salvage values, and reservation values. Our results go through even if the seller cannot commit to the refund amounts, the seller has flexible capacity, or consumers have multi-unit demands.