Chinese College Admissions

Micro MarketDesign

It is a special case of Deferred Acceptance.

Simple recap:

• when $e=1$, it is equivalent to the Boston Mechanism
• when $e=2$, it is equivalent to the Shanghai Mechanism
• when $e=+\infty$, it is equivalent to the Deferred Acceptance

Two-Stage Chinese Admission

In reality, students would not only propose the schools, but also major. and there’s choice for student to choose whether to accept “major transfer”.

Model

• A set of students $I=\{i_1,i_2,\dots ,i_n\}$
• Colleges:
• Majors (which is new): $M=\{m_1,m_2\dots m_n\}$

A matching $\mu :I\to M\cup \{\varnothing \}$ assigns each student a major such that, for each $m^c\in M$, $|{\mu }^{-1}(m^c)|\le q_{m^c}$ if $\mu (i)=\varnothing$

There are two stages:

1. Assign the application of students to colleges.
2. Assign the applicants for each college to majors.

The conclusion is CPM doesn’t respect improvement.

The Rectified Parallel Mechanism.