Warm up by Revelation to Cool down in Competition : Consumer Privacy, Multi-purchase, and Information Sharing

In markets where duopolists supply differentiated products with certain degree of complementarity, not only can each consumer choose to buy one unit from a particular seller (single-purchase), the consumer may also choose to buy from different sellers simultaneously (multi-purchase) for brand diversity. In the latter case, duopolists no long respond to each other by competing head-on for the brand-switching consumer, but they price independently as local monopolies. However, with privacy regulations, sellers may not get access to the information about customers' willingness to pay for making additional purchase from the rival, making them unable to distinguish between competition and independence. We characterize the equilibrium pricing strategies when neither seller has information (competition between third-party sellers), and when only one firm has information (sold by Amazon vs. third-party seller), respectively, and also consider strategic revelation by the informed seller in the latter case. By comparing the equilibrium outcomes under different information structures, we are able to design socially optimal consumer privacy policies in markets that exhibit both brand differentiation and complementarity. In particular, we find that compared to any states/policies that generate incomplete information about consumers, the expected welfare is shown to be the highest when both sellers are fully informed