A worker within a firm, or a researcher within the academia, is required to both cooperate with colleagues in team-projects and to compete with them for career progressions. Hence, within workplaces, individuals need to adapt when switching between tasks characterized by different levels of competitiveness and cooperativeness. We study experimentally whether males and females differently spill over their cooperative behaviour when playing indefinitely repeated Prisoner’s Dilemmas, distinguished by two different levels of the competitiveness cooperativeness index (CCI, Demuynck et al., 2022). Additionally, as the importance placed on competitiveness might differently impacts males and females’ attitudes towards the task, in our Decomposition treatment we separately present its zero-sum component and its common interest component. Besides supporting the efficacy of the CCI, our results provide evidence that females are more likely than males to spill over their cooperative behaviour when switching from a low competitive environment to a high competitive one