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 impulsivebehavior and self-control. Since consumers may pay a premium for an option setthat is less tempting, the seller may offer multiple small menus. Building on thestandard model of adverse selection and second-degree price discrimination, wecharacterize the optimal menu of menus for the seller. In particular, we show thatif consumers are tempted by goods of higher quality, the seller can achieve perfectdiscrimination: consumers' choices appear as if the seller can observe consumers'preferences directly. To achieve this, the seller "decorates" menus by adding itemsthat are never chosen but are tempting to consumers.