The single-step formulation does not account for changes in the student's internal state over In the multi-step formulation, effort put towards studying accumulates in the form of knowledge. We demonstrate this by revisiting the classroom example. The student's grade is then the summation of all scores across time. B.1 Agent's best-response effort sequence A rational agent solves the following optimization to determine his best-response effort policy: { e Recall that the agent's score A dominated effort policy is formally defined as follows: Lemma C.1 Next we look at the complementary slackness condition. From Lemma D.1, we know the form a rational agent's effort Substituting this into Equation 6, we obtain the following characterization of the principal's assessment policy: { E.1 The set of incentivizable effort policies is convex Proof.

A recent line of research investigates how strategic agents may respond to such scoring tools to receive favorable assessments. While prior work has focused on the short-term strategic interactions between a decision-making institution (modeled as a principal) and individual decision-subjects (modeled as agents), we investigate interactions spanning multiple time-steps . In particular, we consider settings in which the agent's effort investment