Overall, the reviewers liked the setting introduced by this paper, and in particular the associated analysis. The main concern was the fit for NeurIPS. After several discussions, the program committee found that this paper is indeed interesting to a part of the NeurIPS community. The reviewers also discussed the concern about relations to online matching, but found that the paper is sufficiently different. I urge the authors to add to the paper to address the reviewer comments, and possible confusions. Consider adding discussions, examples and conclusions. Another point that came up were algorithmic implications, please add to this if possible.