The Impact of Secondary Markets on Selling Blind Boxes with Set Bonuses

Abstract

We develop an analytical framework in which a firm sells a blind box, from which two horizontally differentiated items are randomly drawn. Two types of customers have different valuations for the two items. A customer gains an extra utility, called a set bonus, if she obtains a complete set of items; hence, she may repeat purchases until her expected utility is maximized. We study and compare the selling of blind boxes in two settings, with and without a secondary market. Without a secondary market, customers buy products from the firm only. With the secondary market, customers purchase products from the firm in the first period and then trade the items they have obtained in the second period. We prove that with the secondary market, the firm’s problem is equivalent to a principal-agent problem. We use a linear program and its dual problem to solve the secondary market equilibrium and the firm’s profit. We identify two effects of the secondary market: the growth effect and the incompatibility effect. The former is positive, but the latter is negative. Utilizing the growth effect and reducing the incompatibility effect are not always countervailing, especially when the set bonus is large. We find that the secondary market hurts the firm if and only if customers’ preferences are highly polarized, and the set bonus is positive but small. Our model can easily be extended to a general model in which the blind box includes multiple items. Our main insights still hold in the general model.