In public good provision, privileged groups enjoy the advantage that some of its members find it optimal to supply a positive amount of the public good. However, their inherent asymmetric nature may make the enforcement of cooperative behavior through informal sanctioning harder to accomplish. In this paper we experimentally investigate public good provision in normal and privileged groups with and without decentralized punishment. We find that compared to normal groups, privileged groups are relatively ineffective in using costly sanctions to increase everyone's contributions. Punishment is less targeted towards strong free-riders and they exhibit a weaker increase in contributions after being punished. Thus, we show that privileged groups are not as privileged as they initially seem.