The Value of Flexibility From Opaque Selling

Adam N. Elmachtoub, David D. Yao, Yeqing Zhou

Research output: Working paperAcademic


An opaque product is a product where some secondary attribute is not revealed to the customer until after purchase. Selling opaque products has become popular on e-commerce platforms where the hidden attribute is often color or style, thanks to its obvious advantage in risk pooling the demand. The objective of this study is to quantify the value of consumer flexibility that underlies opaque selling. We consider a setting in which an online retailer sells N products that only differ in a certain secondary attribute, and in addition offers a k-opaque option where customers select k products from which the seller allocates one to the customer. We assume that the prices are exogenously set such that q fraction of the customers select the k-opaque option. We refer to the tuple (q,k) as the degree of opacity, where the flexibility of the system is increasing in both q and k. When q=0 or k=1, our setting reduces to traditional non-opaque selling with no flexibility, and when the degree of opacity is (1,N), this corresponds to a fully flexible scenario where every customer is willing to receive any product.

We find that even with a minimal degree of opacity where q is very small and k=2, the seller can achieve significant cost savings which we quantify precisely. Remarkably, we find that the cost savings from this minimal degree of opacity is on the same order as the fully flexible case corresponding to (1,N). This finding has practical managerial implications, as achieving (1,N) is practically infeasible since it would require substantial incentives by the seller to materialize. Our proofs rely on analyzing a simple balancing policy to allocate products to opaque customers, and explores a novel connection to the balls-into-bins framework. As a byproduct of our analysis, we show that the simple balancing policy is asymptotically optimal. Finally, we provide numerical experiments that suggest our main insight, namely that a small degree of opacity provides advantages akin to a fully flexible system, holds under various extensions of our core setting.
Original languageEnglish
PublisherSocial Science Research Network (SSRN)
Number of pages42
Publication statusPublished - 2019
Externally publishedYes


  • online retailing
  • opaque selling
  • flexibility


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