Autonomous systems, such as drones and rescue robots, are increasingly used during emergencies. They deliver services and provide situational awareness that facilitate emergency management and response. To do so, they need to interact and cooperate with humans in their environment. Human behaviour is uncertain and complex, so it can be difficult to reason about it formally. In this article, we propose IDEA: an adaptive software architecture that enables cooperation between humans and autonomous systems, by leveraging the social identity approach. This approach establishes that group membership drives human behaviour. Identity and group membership are crucial during emergencies, as they influence cooperation among survivors. IDEA systems infer the social identity of surrounding humans, thereby establishing their group membership. By reasoning about groups, we limit the number of cooperation strategies the system needs to explore. IDEA systems select a strategy from the equilibrium analysis of game-theoretic models that represent interactions between group members and the IDEA system. We demonstrate our approach using a search-and-rescue scenario, in which an IDEA rescue robot optimises evacuation by collaborating with survivors. Using an empirically validated agent-based model, we show that the deployment of the IDEA system can reduce median evacuation time by 13.6%.