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Cooperation in economic games breaks down in the absence of enforcement mechanisms. We show that in the Public Goods Game, cooperation can be sustained by altruistic punishment, but not reward. Voluntary leadership occurs frequently in both conditions, but does not affect the dynamics of contributions and enforcement. While pro-socially punishing leaders are perceived as fairer than anti-social leaders, they have a worse reputation than pro-socially rewarding leaders. Thus punishment appears to carry a reputational penalty even when it is pro-social. Contradicting predictions from indirect reciprocity theory, this provides some support for altruistic punishment as strong reciprocity.