Autonomous systems, like drones and self-driving cars, are becoming part of our daily lives. Multiple people interact with them, each one with their own expectations regarding system behaviour. To adapt system behaviour to human preferences, we propose a game-theoretic approach. In our architecture, autonomous systems use sensor data to build a game-theoretic model of their interaction with a human. In this model, human preferences are represented with types and a probability distribution over them. The game-theoretic analysis of this model outputs a strategy, that determines how the system should act to maximise utility, given its beliefs over human types. We showcase our approach in a search-and-rescue (SAR) scenario, with a robot in charge of locating victims. According to social psychology, depending on their identity some people are keen to helping others, and others prioritise their personal safety. These social identities define what a person favours, so we can map them directly to game-theoretic types. We show that our approach enables the SAR robot to take advantage of human collaboration, outperforming non-adaptive configurations in average number of successful evacuations.