How do agents invest strategically under persistent improvement?

The major question that I have about the paper is the one-time effort k. The authors emphasise repeatedly that the effort is a one-time effort, which the agent pays at time t=t_i, say. Such an effort paid changes the agent's qualification from q_{t_i} at time {t_i} to q_{t_{i+1}} at time t_{i+1}, as depicted in equation 1. From equation 1 the authors derive equation 2. Now my question is, for equation 2 to hold for any time t, is it not true that the agent needs to pay effort k again at time t_{i+1}, so that its qualifications will be changed from q_{t_{i+1}} to q_{t_{i+2}} according to equation 1? If what I understand is correct, then equation 3 will need to be revised, so will virtually all subsequent equations and conclusions.

Another issue is that the definition of function C (equation 6) looks arbitrary. It is unclear to me what C is and why we need this function. In fact, the definitions of U (equation 3) and U_d (equation 7) are equally arbitrary, but at least the authors explain what thehy are and why they are defined in that way. I have to point out that though equations 3 and 7 give reasonable definitions for U and U_d, there are no evidence that these are the utility functions real people use.

Such an issue is related to another issue (more serious in my view) in section 7. Basically section 7 only presents a numerical simulation of the relevant equations, instead of proving their correctness in any way. As a matter of fact, it does not really matter what dataset the authors use--even an artificially created dataset would have served this purpose very well, because only the initial conditions are obtained from the dataset. Therefore, I do not see the use of this section. By the way, I do not have the assess to the Exam dataset.

One last point is that the authors use superscript 'T' sometimes to denote 'to the power of T' and sometimes to denote 'transpose'. This is confusing.

1. My major concern is whether the paper fits the scope of the conference or not. It seems to the reviewer that this paper is more suited for a economic journal/conference based on the topic, the way it is presented, and the results. I did not see any discussion in the paper that are related to learning. This is concern drives my rating for this paper.

2. The model formulation is not a generic stackelberg game. The utility function, the dynamics of the model, and the action profile of the agents are defined to study a very specific game. The suggest the authors give a name to the specific game instead of calling it "a novel two-stage Stackelberg model". I was having an impression that the paper studies a generic stackelberg game with delayed and persistent effects when reading the introduction section.

3. The contributions of the results are not significant. For example, the two takeaways from the two theorems in section 6 are 1. the dynamics under forgetting still converges, and 2. the improvement an agent can make under the forgetting mechanism is limited. The two takeaways seem intuitive give the setup of the forgetting mechanism. There are other examples in the previous sections too.

While the model is interesting and could form a reasonable game, I have a major concern about this paper. That is, it is unclear to me how the model is a good reflection of any real world problem. The assumption on the agent qualification dynamics, manipulation/forgetting, and the designer's threshold policy seem to be very strong and artificial. The experiment on real world data also does not reflect whether the modeling is realistic. Hence, I am not sure whether the results derived from this model are particularly useful or insightful for the ICLR audience.