In a recent working paper, “Consumers’ Privacy Choices in the Era of Big Data,” together with job market candidate Sebastian Dengler I study a question that is at the heart of the economics of privacy: Why would consumers with standard preferences facing a monopolistic seller ever anonymize themselves if it comes at a cost?
This paper is driven by two recent empirical developments: first, the increasing ability of sellers, often via the Internet, to obtain many data points about the preferences and characteristics of individual consumers. This enables them to come closer and closer to perfect price discrimination, a case that was dismissed by the literature in industrial organization for many decades due to its strong information requirements. Second, the combined access of sellers to large datasets and the power of algorithms to respond to information about a given consumer quickly. By contrast, many consumers feel overwhelmed by the choices they have to make while shopping and face cognitive constraints.
A guessing game between sellers and buyers
We combine these ingredients in a generic model, where consumers with heterogenous willingness-to-pay for a product can either use a direct sales channel — but expect that the seller will charge them their full willingness-to-pay — or they can spend a cost to hide their identity from the seller, via an anonymous sales channel. For anonymized shoppers, the seller only sees that they anonymized but, for direct shoppers, the seller knows the exact willingness-to-pay.
The tricky part of the model is the guessing game between a consumer and the seller, where the seller sets prices for the product depending on the information she has, and the consumer decides about the sales channel based on his expectation of the prices in both channels. This is implemented as a level-k cognitive hierarchy model. Consumers are characterized by a certain level k, starting at k=0, which stands for the number of iterations they can predict the seller’s best pricing response. The traditional assumption of unlimited cognitive sophistication is nested in this model for k = ∞. The seller, having access to big data and powerful algorithms, has higher k than consumers.
Who anonymizes — and why? Microfounding privacy choices
The information assumptions turn out to be crucial for the model’s results. We show that consumers with high willingness-to-pay have an incentive to anonymize, whereas those with low willingness-to-pay use the direct channel, get perfectly-discriminated prices, and walk home with zero consumer surplus. Anonymous shoppers, however, do not (fully) predict that the seller understands that their cost of anonymization are sunk when deciding about a purchase. Therefore, the seller will increase the price in the anonymous market segment by the cost of anonymization, which leaves some consumers with negative and others with positive consumer surplus. If consumers understand this threat (at k=1), those with moderate willingness-to-pay also prefer the direct channel. This process is repeated with increasing k of consumers: the anonymous market unravels level by level. Importantly, it unravels already for finite k. That is, unlimited sophistication of consumers is a sufficient but not necessary condition for the breakdown of the anonymous channel. In essence, the higher consumers’ sophistication, the fewer consumers choose to anonymize, and the lower is aggregate consumer surplus. On the other hand, the seller benefits from this unraveling as her profits are maximized on consumers in the direct channel. We also show that k and the cost of anonymization interact in equilibrium: for a given k, increased anonymization costs also lead to a smaller anonymized market and, finally, to the breakdown of that segment.
The key contribution of this paper is to show that and when a costly anonymous sales channel is used in equilibrium. This offers a micro-foundation of privacy choices—the existence of privacy preferences is often assumed in other works.
Moreover, this paper has clear and important policy implications. Considering that consumers’ level of sophistication is exogenous, the key parameter that can be influenced by policy makers is the cost of anonymization. We show that consumers fare best if these costs are zero, whereas the seller maximizes profits if no consumer anonymizes, due to prohibitive anonymization costs. From a total welfare perspective, these two cases have identical consequences. Hence, the model suggests that those authorities focusing on consumers’ interests invest in cheaper and easier-to-use privacy-protective tools and legislate that the default sales channel be the anonymous one. That is, to allow sellers to offer consumers registration/tracking technologies, in exchange for a price discount, but to prohibit that consumers are tracked and targeted by default and have to anonymize for a cost (which is standard today).