We present an economy of farmers where food aid is warranted due to poverty traps triggered by nonconvex production sets. We model a food‐aid intervention as a dynamic game between a food‐aid manager and the farmers in a context of asymmetrical information. The food‐aid manager is motivated by a relief objective and targets farmers suffering the poverty trap. The food‐aid manager uses a self‐targeting mechanism by providing the aid through a food wage in exchange for participation in the intervention's activities. Guided by the relief objective and targeting constraint, he fixes the food wage equal to the reservation wage of the farmers not suffering the poverty trap. Dependency traps will then happen every time there is a considerable technological and nutritional gap between farmers who are in and out of the poverty trap. When there is a gap, poor farmers earn more working for the reservation wage of the well‐off farmers than by working in their own farm. Dependency can be overcome only if the food‐aid program allows farmers to upgrade their productive technologies and catch up with those farmers who are out of the poverty trap.