The increase of space debris means that active space debris removal is becoming more relevant. An active debris removal mission would have a positive effect (or risk reduction) for all satellites in the same orbital band. This leads to a dilemma: each space agency has an incentive to delay its actions and wait for others to respond. We model this scenario as a non-cooperative game between self-interested agents in which the agents are space agencies. Using a high-fidelity simulator we estimate payoffs to agents for different combinations of actions taken, and analyse the resulting game in terms of best-response dynamics and (Nash) equilibria. Contrary to the urgency of the space debris dilemma there has not been much attention to this problem in scientific circles. To the best of our knowledge we are the first to consider this dilemma in the context of multi-agent strategic decision making using empirical game theoretic techniques.