Divisive by design shaping values in optimal mechanisms

We study a principal who allocates a good to agents with private, independently distributed values through an optimal mechanism. The principal can strategically shape these value distributions by modifying the good's features, which affect agents' valuations. Our analysis reveals that optimal designs are frequently divisive - creating goods that appeal strongly to specific agents or agent types while being less valued by others. These divisive designs reduce information rents and increase total surplus, even though they reduce competition. Even when total surplus is constrained, some divisiveness in designs remains optimal.