A new study, "Divisive By Design: Shaping Values in Optimal Mechanisms," by Anja Prummer from Freie Universität Berlin and Berlin School of Economics, and Francesco Nava from London School of Economics, examines how a principal—someone selling a good or allocating a resource—can strategically implement features of a good to alter its value for potential buyers. The main goal is to maximize the principal's revenue.
The paper introduces the concept of divisive designs— goods intentionally crafted to be highly appealing to certain (types of) agents, while being less attractive to others. Take, for example, a bureaucrat responsible for allocating a plot of land. They might consider adding specific features like environmental restrictions or ensuring highway access. Environmental restrictions could increase the value of the land for some companies seeking a production site, while others may not be able to meet them due to their production technology, rendering the plot useless. Another interested buyer, a water skiing entrepreneur values green technologies and would benefit from the added restrictions, while a school superintendent looking for a plot for a new school might be unaffected by the regulation. Conversely, granting highway access might reduce the land's value for the school superintendent due to increased pollution, but significantly boost it for a production site due to improved transportation. This example illustrates how features of a good may affect buyers depending on their chracteristics. Moreover, it demonstrates how a design can be divisive, making a good more valuable to some and less to others.
The research shows that such divisiveness increases the principal’s revenue as it helps the principal in two key ways. First, divisive designs increase the overall expected value (or surplus) by creating a product that is highly valuable to at least one buyer, enabling the principal to charge a higher price. Second, these designs make agents’ valuations more predictable. To infer buyers’ valuations and allocate the good optimally, the principal must incentivize buyers to reveal their private information. Divisive designs reduce the cost of eliciting this information, thereby increasing the principal’s revenue.
Even when surplus is constant, some level of divisiveness remains optimal. The study highlights that features leading to extreme distributions—where a good is either highly valued or not at all by different agents—are especially effective. They help the principal to identify and segment agents who might initially seem similar. Returning to our previous example, the bureaucrat will benefit from imposing specific eco-friendly policies that attract certain companies while deterring others.
More broadly, "Divisive by Design" offers a formal framework for product design in various contexts. For instance, it applies equally well to how an artist might create work that strongly appeals to a specific group of collectors, demonstrating that targeting particular types, rather than aiming for universal appeal, is an optimal strategy to generate revenue.
About the authors
Anja Prummer
Professor of Microeconomics at Freie Universität Berlin and member of the Berlin School of Economics. Her research revolves around determinants of social structures, how they constrain economic decisions and how they can be amended.
Francesco Nava
Assistant Professor of Economics at London School of Economics. His expertise covers Economic Theory, Social Networks and Industrial Organisation.
