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SCREENING OF BUDGETED AGENTS

Hedyeh Beyhaghi, Modibo Camara, Jason Hartline,

Aleck Johnsen, Sheng Long

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Office of admissions

timeline

📚⏰ or

🙅‍♀️

Admit students

Imagine a screening scenario.

You’re are an admissions officer at some school. Admitting high skill students give you positive utility, so you want to admit high-skill students.

As the uninformed party, you fix a test and design a score-based admissions policy.

After seeing your admissions policy, students will then decide how much effort they will put into preparing for the test.

Afterwards, students will obtain their scores, which we model score as a product between their skill and and the amount of time they have spend on preparing for the test, or in other words, their effort.

After seeing the student’s scores, you will then admit students based on your admissions policy.

One thing to note is that we model students as having constraints on their budgets, meaning that students cannot put more effort than what their budget allows.

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Why should we care about budgets?

Practical motivation: not all students have the same access to preparation for the exam

Budgets are “constraining” 🡪 score does not exactly identify skill

Now, the reason that we model students as having budgets, is because

One, we believe that this is what we face in real life. Students preparing for the test might not have all the access to the same resources.

Some students might need to work three or four shifts to cover for their living expenses, while others don’t. Working three or four shifts a day means that you won’t be able to have as much time to study and prepare for tests as you would like to.

The second reason we care about budgets, is that as the admissions officer, you only get to observe a student’s score, even though what you truly care about, is their skill.

But since budgets are constraining, so to speak, standard approaches will not help us identify a student’s skill, and this is going to challenge our goal of admitting students with high skills.

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Example population

Max score:

60%

Max score:

82%

Max score:

93%

Max score:

80%

Budget

Skill

⏳⏳

⏳

💪

🤔 What would be a good admissions policy?

💪💪

For this talk, let’s consider the simplest case, when a student either has a high or low skill, and a high or low budget.

This will give us four types of students.

For a random student, the admissions officer does not know their skill, nor their budget on effort.

The admissions officer also does not know what their scores will be, before they’ve decided an admissions policy.

However, for each type of student, the admissions officer does know the maximum potential score. In this example, the admissions officer knows that if a student has a high skill and a high budget, then the maximum potential score they can achieve is 93%.

Recall that admitting high-skill students gives the admissions officer positive utility.

Given that this is our goal, what would be a good admissions policy, that also considers the fact that students have different budgets? �

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100

0

90

Max score:

60%

Max score:

82%

Max score:

93%

Max score:

80%

⏳⏳

⏳

💪 💪

💪

😟

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100

0

80

Max score:

60%

Max score:

82%

Max score:

93%

Max score:

80%

⏳⏳

⏳

90

💪 💪

💪

😟

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Behavior under a multi-track policy:

Max score:

60%

Max score:

82%

Max score:

93%

Max score:

80%

⏳⏳

⏳

100

0

💪 💪

💪

90

72

Admit with certainty

Admit with Pr. 0.8

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The paper

Thank you for listening!