One of the best-known and most replicated laboratory results in behavioral economics is that bargainers frequently reject low offers, even when it harms their material self-interest. This finding could have important implications for international negotiations on many problems facing humanity today, because models of international bargaining assume exactly the opposite: that policy makers are rational and self-interested. However, it is unknown whether elites who engage in diplomatic bargaining will similarly reject low offers because past research has been based almost exclusively on convenience samples of undergraduates, members of the general public, or small-scale societies rather than highly experienced elites who design and bargain over policy. Using a unique sample of 102 policy and business elites who have an average of 21 y of practical experience conducting international diplomacy or policy strategy, we show that, compared with undergraduates and the general public, elites are actually more likely to reject low offers when playing a standard "ultimatum game" that assesses how players bargain over a fixed resource. Elites with more experience tend to make even higher demands, suggesting that this tendency only increases as policy makers advance to leadership positions. This result contradicts assumptions of rational self-interested behavior that are standard in models of international bargaining, and it suggests that the adoption of global agreements on international trade, climate change, and other important problems will not depend solely on the interests of individual countries, but also on whether these accords are seen as equitable to all member states.