Group membership is a powerful determinant of social behaviour in a variety of experimental games. Its effect may be channelled primarily via the beliefs of group members, or directly change their social preferences. We report an experiment with a prisoner’s dilemma with multiple actions, in which we manipulate players’ beliefs and show that group identity has a consistent positive effect on cooperation only when there is common knowledge of group affiliation. We also test the robustness of the minimal group effect using three different manipulations: one manipulation fails to induce group identity, and we observe an unsystematic effect of group membership when knowledge of affiliation is asymmetric.
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