Strong negative reciprocity, that is, sanctions imposed on norm violators at the punisher’s own expense, has powerful cooperation-enhancing effects in both real-life and experimental game situations. However, it is plausible that punishment may obtain alternative roles depending on social context and the personality characteristics of participants. We examined the occurrence of punishing behavior among 80 subjects in a strongly competitive Public Goods game setting. Despite the punishment condition, the amount of the contributions decreased steadily during the game. The amount of contributions had no significant effect on received and imposed punishments. The results indicate that certain social contexts (in this case, intensive competition) exert modifying effects on the role that punishment takes on. Subjects punished each other in order to achieve a higher rank and a financially better outcome. Punishment primarily functioned as a means of rivalry, instead of as a way of second-order cooperation, as strong reciprocity suggests. These results indicate the need for the possible modification of the social conditions of punishment mechanisms described by the strong reciprocity theory as an evolutionary explanation of human cooperation.