1. Consider the following college admission matching problem. There are four students, Alice, Bob, Carol, and Daniel. There are three colleges, East State, West State, and State U. Quotas are two students for East State and one apiece for West State and State U. No student ranks "no college" higher than one of the three colleges. Every student is acceptable to every college. The four students rank the colleges as follows:

1. Alice prefers State U to East State to West State.
2. Bob prefers West State to East State to State U.
3. Carol prefers East State to State U to West State.
4. Daniel prefers East State to West State to State U.

The three colleges have responsive preferences over cohorts, based on the following rankings of the individual students:

• Both East and West State prefer Alice to Bob to Carol to Daniel.
• State U prefers Carol to Alice to Bob to Daniel.
• Questions:
• 1. Compute step-by-step what happens in the deferred-acceptance algorithm with colleges proposing to students.
• 2. Find a match that each college strictly prefers than the one you find in 1).
• 3. The "better" match in 2) is of course not stable. Explain why this is true.