A Qualitative Game of Interest Rate Adjustments with a Nuisance Agent

Round 1

Reviewer 1 Report

The review is attached

Comments for author File: Comments.docx

Author Response

Dear Referee,

We are also grateful for your positive and insightful reports. We have revised the paper in accordance with your comments and suggestions. Below we provide a list of the changes to the current draft.

Comment: In the row 2 should be “qualitative”.

Response: We have changed the word to “qualitative”.

• Comment: It would be more convenient to enumerate the control variables of the domestic bank and the foreign bank, their feasible domains, and their explanations in one place.
Response: To address this comment, we have added two new paragraphs to the paper.
- On page 5, we have included the following sentences: “In our model, there are also two players with coupled dynamics. The first player is the domestic bank of a small open economy, whose objective is to keep the domestic economy in the closed set K (i.e., avoid being in K’s complement for all t ∈ Θ). The other player is the bank of a foreign economy, which pursues its own target that is unrelated to K. The dynamics are coupled through the actions of the foreign bank, which affect the domestic economy’s position. Hence, in seeking to remain in K, the domestic player must react to the foreign player’s actions.”

- Also, on page 7, we have added the following paragraph: “In the parlance of optimal control and dynamic games, the vector [y(t), π(t), i(t), q(t)], t ∈ Θ is the state vector for the domestic central bank. The vector’s domain is R4 ⊃ K. The control variable in this model is u(t) ∈ U ⊂ R. The noise (disturbance) input into this model is the real interest rate of the large (foreign) economy, which is controlled by the foreign central bank. This input will be introduced in (11).”

• Comment: Just after the problem statement the authors go to the interpretation of a 3D projection of a 4D kernel by means of a specialized software, and the economic conclusions. It seems that the mathematical solution of the problem should be characterized in more details (may be a couple of phrases from Appendix C).

Response: We have followed the referee’s suggestion and moved what used to be Appendix C1 to a new subsection 5.1 on page 11 titled “A method for the determination of viability kernels”.

 

Reviewer 2 Report

I appreciate the documentation made by the authors in writing this article proposal, this can be seen both in the foray into the current state of knowledge from the first part and from the mentioned bibliography.

I also note the applicative part of this article proposal and I favorably appreciate this way of elaborating the applicative part starting from the development of some models.

Consequently, I recommend the publication of this article proposal.

Author Response

Dear Referee,

We thank you for an overall favourable opinion of our paper. We believe that the changes we have made have improved it. 

The changes we have made to the paper are in blue font.