Strategy-Proofness & Manipulation

You are student s1. Can you improve your outcome by misreporting your preferences? Try under the Boston Mechanism, then see why it fails under Deferred Acceptance.

Setup

Challenge: Under the Boston Mechanism, your truthful report gets you school C. Can you reorder your submitted preferences to get a better outcome?

Student Preferences (True)

s1★ A > B > C > D YOU

s2A > B > D > C

s3A > C > B > D

s4B > A > C > D

s5B > D > A > C

School Priorities & Quotas

A[q=2]s3 > s2 > s1 > s4 > s5

B[q=2]s1 > s4 > s5 > s2 > s3

C[q=1]s3 > s1 > s2 > s5 > s4

D[q=1]s5 > s2 > s4 > s1 > s3

Your Submitted Preferences (drag to reorder)

True: A > B > C > D

☰1.School A
☰2.School B
☰3.School C
☰4.School D

Attempt History

Theorem (Roth, 1982): Strategy-Proofness of DA

Under the student-proposing Deferred Acceptance algorithm, reporting true preferences is a dominant strategy for every student. No student can obtain a better outcome by misreporting preferences, regardless of what other students report.

In contrast, the Boston Mechanism is manipulable: students can benefit by strategically ranking "safe" schools higher than their true favorites, because the mechanism permanently assigns seats in each round.

Roth, A.E. (1982). "The Economics of Matching: Stability and Incentives." Mathematics of Operations Research, 7(4): 617-628.