1. There are six students, A, B, C, D, E, and F, and three colleges, X, Y, and Z, each with room for two students. The student preferences are given in Table 1 and the college preferences are given in Table 2.
table 1
| A |
B |
C |
D |
E |
F |
| X |
X |
Z |
Z |
Y |
X |
| Y |
Y |
Y |
Y |
X |
Z |
| Z |
Z |
X |
X |
Z |
Y |
| X |
Y |
Z |
| B |
A |
A |
| A |
F |
B |
| C |
C |
C |
| D |
E |
F |
| E |
D |
D |
| F |
B |
E |
table 2
a. Work out the matching generated by SODA. Demonstrate that it is stable.
b. Work out the matching generated by CODA. Demonstrate that it is stable.
2. There are six students, A, B, C, D, E, and F, and three colleges, X, Y, and Z, each with room for two students. The test scores are displayed in Table 3 and the student preferences are given in Table 4.
| Student |
Quantitative Score |
Verbal Score |
| A |
90 |
80 |
| B |
85 |
90 |
| C |
80 |
70 |
| D |
75 |
60 |
| E |
70 |
75 |
| F |
65 |
85 |
Table 3
| A |
B |
C |
D |
E |
F |
| X |
X |
Z |
Z |
Y |
X |
| Y |
Y |
Y |
Y |
X |
Z |
| Z |
Z |
X |
X |
Z |
Y |
Table 4
a. Work out the matching determined by the CODA if college X were to use the quantitative score and Y and Z each used the verbal test score.
b. Assume that colleges X and Y use the quantitative test score and Z uses the verbal score. Work out the matching determined by the CODA.