It is often taken for granted that social identity and the relative strength of group identities matter for how public resources are allocated. We present an experiment that enables us to identify the causal effects of social identity and the relative strength of group identities over the allocation of a windfall profit. Specifically, we utilize a simplified version of the Baron-Ferejohn (henceforth BF) Model to derive a prediction on how rational agents allocate such a windfall profit. In the experiment, subjects are placed into groups of five and bargain over the allocation of a windfall profit using the BF mechanism. According to the minimal group paradigm, subjects’ social identity was induced by conducting a tournament version of the Klee-Kandinsky task before the bargaining stage. Here we distinguish three treatment conditions, namely bargaining in homogenous groups (only Klees’, only Kandinskys’), in heterogeneous groups (3 Klees’ vs. 2 Kandinskys’ and vice versa), and bargaining in a control group in which subjects are not informed about their Klee-Kandinsky identity. Our experimental results provide strong evidence on the ambiguous effect of social identity. While homogenous groups agree on a fairer allocation, there is robust evidence for in-group favoritism and out-group discrimination, compared to the control treatment. Contrary to previous research studying social identity and allocation preferences, this study shows that a collective decision-making mechanism that allows targeting allocation decisions by social groups (here BF) unleashes both the positive and negative social identity consequences for social welfare.