To avoid the dangerous consequences of climate change, humans need to overcome two intertwined conflicts. First, they must deal with an intra-generational conflict that emerges from the allocation of costs of climate change mitigation among different actors of the current generation. Second, they face an inter-generational conflict that stems from the higher costs for long-term mitigation measures, particularly helping future generations, compared to the short-term actions aimed at adapting to the immediate effects of climate change, benefiting mostly the current generation. We devise a novel game to study this multi-level conflict and investigate individuals’ behavior in a lab experiment. We find that, although individuals reach sufficient cooperation levels to avoid adverse consequences for their own generation, they contribute more to cheaper short-term than to costlier long-term measures, to the detriment of future generations. Simple “nudge” interventions, however, may alter this pattern considerably. We find that changing the default contribution level to the inter-generational welfare optimum increases long-term contributions. Moreover, providing individuals with the possibility to commit themselves to inter-generational solidarity leads to an even stronger increase in long-term contributions. Nevertheless, the results also suggest that nudges alone may not be enough to induce inter-generationally optimal contributions.