Cooperation is indispensible in human societies, and much progress has been made towards developing mechanisms to promote pro-social decisions. Economists have focused on punishment and rewards, typically finding that cooperation can be sustained only at substantial efficiency cost. At the same time, biologists have long recognized that cooperation, especially food sharing, is typically efficiently organized in groups living on wild foods. Despite its evident importance, the source of this efficiency remains controversial. Drawing on evolutionary psychology, we hypothesize that efficient sustained cooperation relies on male preferences for unique and displayable rewards (trophies) out of competition. Further, here we show with a controlled laboratory experiment that efficient cooperation emerges in a generosity competition with trophy rewards. The same environment with equally valuable but non-unique and non-displayable rewards fails to result in cooperation. Moreover, we find that under trophy rewards both the proportion and contributions of co-operator “types” significantly increases in males. In contrast, we find no evidence that female generosity is modulated by trophies. Our results open new paths to promoting cooperation in human groups efficiently. This could have important impact in any domains where voluntary compliance matters, including relations between spouses, employers and employees, as well as economic exchange and conformity to legal standards.