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The rapid development of drone technology is leading to more and more use cases being proposed. In response, regulators are drawing up drone traffic management frameworks. However, to design solutions that are efficient, fair, simple, non-manipulable, and scalable, we need market design and AI expertise. To this end, we introduce the drone traffic management problem as a new research challenge to the market design and AI communities. We present five design desiderata that we have derived from our interviews with stakeholders from the regulatory side as well as from public and private enterprises. Finally, we provide an overview of the solution space to point out possible directions for future research.