Classical game theory struggles to explain how rational players should decide between a number of social conventions, even if some yield higher individual payoffs than others. Thus, on a population level a group or society may be stuck in using one convention when there exist alternative and potentially more beneficial ones. Using an agent-based model the current study examines how convention shifts from less to more beneficial conventions can come about. To investigate this, we use the concept of team reasoning, a mode of reasoning in which actors maximise the utility of a group rather than their own. Unlike other social decision-making mechanisms, such as forms of imitation, team reasoning enables the spread of a more profitable convention through a population even if no global knowledge about the population is available to agents.