2. Consider the problem of assigning students to schools. There are three students: 1,
2 and 3; and three schools: A, B and C each with one available spot. The students'
1
preferences and the schools' priority rankings are
P(1) = A, B, C P(A) = 1,2,3
P(2) = A, B, C P(B) = 2,1,3
P(3) = B, A, C P(C) = 1,2,3
(a) Write down the steps and outcome of the student-proposing deferred acceptance
algorithm (assuming students and schools submit their true preferences).
(b) Consider the immediate acceptance algorithm. This is like the deferred acceptance
algorithm except that any proposal that is not reject is accepted and the matched
pair exit the market. See below for a formal description. Write down the steps
and outcome of the student-proposing immediate acceptance algorithm (again,
assuming students and schools submit their true preferences).
(c) When running the immediate acceptance algorithm, is it in the best interest for
all students to submit their true preferences? Is there a false preference list one
of the students can submit that gets them a better match (if yes, give an example
of such a list)?
