*In this paper, we study the designs that an online platform can implement to regulate the interactions among its users. We uncover a possible rationale for the design of a marketplace in which a default seller (i.e., prominent seller) is chosen by the platform and how this choice allows the platform to reduce, and possibly remove, a vertical negative externality. Designing a contest for assigning prominence leads to a reduction in the retail prices and allows the platform to set a commission rate per-unit close to the monopoly one. Compared to direct prominence allocation designs, letting sellers compete for prominence makes the intermediary and consumers better-off. If there is enough vertical differentiation among sellers, the high-quality seller may also benefit from competing for prominence, while the low-quality seller is unambiguously worse off.

**In our model, players contribute to two local public goods for which they have different tastes and sponsor costly social connections to enjoy the provision of their neighbors. In any Nash equilibrium, either there are two large contributors who might free ride on each other, or several contributors whose neighborhood of free riders does not overlap. As linking costs increase, in the contribution maximizing equilibrium players link to large contributors closer to their own type, i.e., homophily increases. Polarization increases if links are cheap to begin with, and decreases otherwise. Moreover, if moderate agents emerge as large contributors, welfare increases while polarization decreases in societies with low extremism.