We first thank all reviewers for their thoughtful comments, and we wish everyone health during these hard times

We first thank all reviewers for their thoughtful comments, and we wish everyone health during these hard times. We acknowledge the simplicity in our linear demand and reference price update models. These references are also discussed in Section 2 of the paper. The gradient of revenue can be calculated using estimated elasticity, observed sales (i.e. Assumption 1 is invoked in all theorems and lemmas of Section 5, and we will clearly state this in the revised paper. In the proof of Lemma 3.2, we show that This means if firms are willing to consider both prices near zero and those sufficiently large, Assumption 1 holds.