What is the impact of individual characteristics of participants on international negotiations? Although research on international relations and negotiations has examined different negotiation strategies and bargaining dynamics extensively, we know less about how factors such as negotiator gender and age may shape negotiation dynamics. We theorize that because individuals face different expectations and assessments about their competence due to their identity characteristics, they also have incentives to adjust their rhetoric and strategies to demonstrate their capabilities as negotiators. This ``competence signaling" can lead individuals from underrepresented groups to adopt less cooperative strategies. Leveraging novel data on the identities of negotiators in more than 3,500 statements at the Council of the EU in 2011-2016, we investigate whether different kinds of individuals employ systematically different strategies when negotiating EU policy. Our findings show that women are less likely to indicate flexibility and willingness to compromise in negotiations than men, as well as less likely to be informal in their negotiation rhetoric. Building on existing work on international relations, psychology, and business studies, we investigate empirically the individual-level sources of negotiation strategies with implications for international cooperation.