The COVID‐19 pandemic points to the need for scientists to pool their efforts in order to understand this disease and respond to the ensuing crisis. Other global challenges also require such scientific cooperation. Yet in academic institutions, reward structures and incentives are based on systems that primarily fuel the competition between (groups of) scientific researchers. Competition between individual researchers, research groups, research approaches, and scientific disciplines is seen as an important selection mechanism and driver of academic excellence. These expected benefits of competition have come to define the organizational culture in academia. There are clear indications that the overreliance on competitive models undermines cooperative exchanges that might lead to higher quality insights. This damages the well‐being and productivity of individual researchers and impedes efforts towards collaborative knowledge generation. Insights from social and organizational psychology on the side effects of relying on performance targets, prioritizing the achievement of success over the avoidance of failure, and emphasizing self‐interest and efficiency, clarify implicit mechanisms that may spoil valid attempts at transformation. The analysis presented here elucidates that a broader change in the academic culture is needed to truly benefit from current attempts to create more open and collaborative practices for cumulative knowledge generation.