QUestion 4 Economic matching

4. Consider a college's dormitory allocation problem. There are 5 dorm rooms: a, b, c, d, e and 5 students, 31,82,83, s4, 35. Student 31 currently occupies room a and student 9.: S4 currently occupies room :3. Students' preferences are as follows: 51 $2 $3 54 $5 a c b b b b d c c c c e d d. a d a e e e b a Is the random serial dictatorship mechanism strategyproof in this setting? [5 points] Is the random serial dictatorship mechanism individually rational in this setting? [5 points] Calculate the result of serial dictatorship with order of dictators $1, 32, 33,34, 35 and with the order 35, 34, 33.32.51. For each of the resulting assignments, is it efficient? [5 points] Calculate the result of WC with order of dictators 3534,33, 5'2, 5'1. Is the result efficient? [6 points] Can one of the students manipulate TfC by misreporting her preferences? [4 points]