||The human ability to establish cooperation, even in large groups of genetically unrelated strangers, depends upon the enforcement of cooperation norms. Third-party punishment is one important factor to explain high levels of cooperation among humans, although it is still somewhat disputed whether other animal species also use this mechanism for promoting cooperation. We study the effectiveness of third-party punishment to increase childrenís cooperative behavior in a large-scale cooperation game. Based on an experiment with 1,120 children, aged 7 to 11 y, we find that the threat of third-party punishment more than doubles cooperation rates, despite the fact that children are rarely willing to execute costly punishment. We can show that the higher cooperation levels with third-party punishment are driven by two components. First, cooperation is a rational (expected payoff-maximizing) response to incorrect beliefs about the punishment behavior of third parties. Second, cooperation is a conditionally cooperative reaction to correct beliefs that third party punishment will increase a partnerís level of cooperation.