In this paper, the authors elucidate the min-max based optimal transport theory. In recent years, min-max based OT is widely studied and this theorem would help to understand the theoretical aspects of min-max based OT methods. All reviewers agree that the proposed approach is interesting. On the other hand, due to the lack of clarity, the authors must revise the paper thrououtly based on the reviewers comments to improve the clarity. In addition, as you promised in the rebuttal letter, I strongly encourage authors to add more numerical experiments to backup your theory. Therefore, I would recommend this paper as weak accept.