Optimal menu of menus with self-control preferences

This paper studies how a seller should design its price schedule when consumers' preferences are subject to temptation. As in Gul and Pesendorfer (2001), consumers exercise costly self-control to some degree and foresee their impulsive behavior and self-control. Since consumers may pay a premium for an option set that is less tempting, the seller may offer multiple small menus. Building on the standard model of adverse selection and second-degree price discrimination, we characterize the optimal menu of menus for the seller. In particular, we show that if consumers are tempted by goods of higher quality, the seller can achieve perfect discrimination: consumers' choices appear as if the seller can observe consumers' preferences directly. To achieve this, the seller "decorates" menus by adding items that are never chosen but are tempting to consumers.