We thank the reviewers for their helpful comments. Due to space limitations, we comment here on major questions and suggestions. Reviewer 1: We thank you for appreciating the balance between rigor and intuition. "why pure Nash equilibria, better response dynamics..." We employ the one-shot model as an approximation of "can the pure Nash equilibrium be reached using best response dynamics?" We will add that to the paper, thanks.

We thank the reviewers for their helpful comments. Due to space limitations, we comment here on major questions and suggestions. Reviewer 1: We thank you for appreciating the balance between rigor and intuition. "why pure Nash equilibria, better response dynamics..." We employ the one-shot model as an approximation of "can the pure Nash equilibrium be reached using best response dynamics?" We will add that to the paper, thanks.