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Reputation and punishment are two distinct mechanisms that facilitate cooperation among strangers. However, empirical research on their effectiveness is mainly limited to relatively small groups and does not address how they enhance cooperation in relatively larger groups. We address this gap in the literature by testing hypotheses from competing perspectives about the extent to which reputation-based partner choice and punishment enhance cooperation in both small and large groups. Prior work recognizes that an increase in group size is accompanied by a change in the incentive structure, which determines whether the temptation (extra benefit for each person from non-cooperation over cooperation, regardless of others’ choices) or gain (extra benefit for each person from full cooperation over full non-cooperation) remains constant or varies with group size. Thus, we first test how group size affects cooperation when temptation or gain increases with group size (Study 1), and then move on to testing predictions on the effectiveness of reputation and punishment across different group sizes (Study 2). In Study 1 (N = 820), we randomly assigned participants to play an online one-shot public goods game in groups of 4, 20, or 40, while keeping the marginal group return or marginal per capita return fixed across groups, in which case the temptation or gain increased with group size. In Study 2 (N = 1,132), we further compared a public goods situation involving a punishment or reputation mechanism with an anonymous situation across group sizes, while the marginal group return was fixed across groups. Overall, we found that when temptation …