While the collective benefits of data sharing for science are clear, sharing data is not yet common practice in many research areas. Furthermore, there is scant knowledge on contexts and consequences of incentivising data sharing by funding agencies. Here, we built an abstract agent-based model to investigate the potential effect of funding selectivity and incentives for data sharing on the uptake of data sharing by academic teams which adapt strategically to resources. Our results suggest that more competitive funding schemes lead to higher rates of data sharing in the short run but lower uptake of data sharing in the long run than less selective funding. Attempts to reform systems of reward and recognition to foster Open Science practices should carefully consider the actual impact of measures and their potential long-term side effects.