Numerous studies suggest that communication may be a universal means to mitigate collective action problems. In this study, we challenge this view and show that the communication structure crucially determines whether communication mitigates or intensifies the problem of collective action. We observe the effect of different communication structures on collective action in the context of finitely repeated intergroup conflict and demonstrate that conflict expenditures are significantly higher if communication is restricted to one's own group as compared to a situation with no communication. However, expenditures are significantly lower if open communication within one's own group and between rivaling groups is allowed. We show that under open communication intergroup conflicts are avoided by groups taking turns in winning the contest. Our results do not only qualify the role of communication for collective action but may also provide insights on how to mitigate the destructive nature of intergroup conflicts.