Although third-party punishment plays a crucial role in the maintenance of reciprocal cooperative relationships in human society, for various reasons such punishment is not consistently levied even when it may be appropriate to do so. The present study investigated the effects of external incentives and psychopathy on non-intervention in a situation where third-party punishment would be warranted. Forty participants who completed a measure to assess psychopathy participated in an experiment in which they had to choose either to punish social norm violators as third-parties, to help victims, or to refrain from correcting the unfair outcomes, under conditions where non-intervention was either rewarded or punished. Results showed that frequency of non-intervention decreased in a condition where there were assured punishments with non-intervention, with participants more likely to intervene in the unfair situation as a third-party. On the other hand, frequency of non-intervention increased when there was assured rewards for non-intervention, with many participants failing to correct the unfair outcomes. Additionally, this tendency was accentuated in high psychopathy individuals. The implications of these results for future research on the cultivation and continuation of reciprocal human relationship is discussed.