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

A principal seeks production of a good within a limited time-frame with a hard deadline, after which any good procured has no value. There is inherent uncertainty in the production process, which in light of the deadline may warrant simultaneous production of multiple goods by multiple producers despite there being no marginal value for extra goods beyond the maximum quality good produced. This motivates a crowdsourcing model of procurement. We address efficient execution of such procurement from a social planner's perspective, taking account of and optimally balancing the value to the principal with the costs to producers (modeled as effort expenditure) while, crucially, contending with self-interest on the part of all players. A solution to this problem involves both an algorithmic aspect that determines an optimal effort level for each producer given the principal's value, and also an incentive mechanism that achieves equilibrium implementation of the socially optimal policy despite the principal privately observing his value, producers privately observing their skill levels and effort expenditure, and all acting only to maximize their own individual welfare. In contrast to popular "winner take all" contests, the efficient mechanism we propose involves a payment to every producer that expends non-zero effort in the efficient policy.