1.Consider an assignment market with objects a,b,c,d,e and 5 agents, where agents have preferences over objects, and objects have priorities over agents. a) If the priority and preference profiles are as specified above, find the matching selected by the TTC with Priorities mechanism. Display the steps. ( 20 points) b) Find an agent order which, if used as a basis for a Serial Dictatorship, gives the same assignment as the TTC with Priorities mechanism in part a) at the given preference profile. Is there always such an agent order for an assignment obtained by the TTC with Priorities mechanism? Explain. (10 points) c) Specify the priority profile for the YRMH-IGYT mechanism with agent order (1,2,3,4,5) if agent 2 is endowed with object c and agent 3 is endowed with object a, while the other agents are not endowed. Find the corresponding assignment when the preference profile is the one provided on page 1 . Is the assignment individually rational? (20 points) d) Now assume that the priority profile specified in part c) corresponds to a TTC with Mixed Endowments mechanism. Which private endowments are possible, given this priority profile? (5 points) e) Let the assignment be (e,b,c,a,d) when the preference profile is the one provided on page 1 . Is this assignment Pareto efficient? Justify your answer. (5 points) 1.Consider an assignment market with objects a,b,c,d,e and 5 agents, where agents have preferences over objects, and objects have priorities over agents. a) If the priority and preference profiles are as specified above, find the matching selected by the TTC with Priorities mechanism. Display the steps. ( 20 points) b) Find an agent order which, if used as a basis for a Serial Dictatorship, gives the same assignment as the TTC with Priorities mechanism in part a) at the given preference profile. Is there always such an agent order for an assignment obtained by the TTC with Priorities mechanism? Explain. (10 points) c) Specify the priority profile for the YRMH-IGYT mechanism with agent order (1,2,3,4,5) if agent 2 is endowed with object c and agent 3 is endowed with object a, while the other agents are not endowed. Find the corresponding assignment when the preference profile is the one provided on page 1 . Is the assignment individually rational? (20 points) d) Now assume that the priority profile specified in part c) corresponds to a TTC with Mixed Endowments mechanism. Which private endowments are possible, given this priority profile? (5 points) e) Let the assignment be (e,b,c,a,d) when the preference profile is the one provided on page 1 . Is this assignment Pareto efficient? Justify your answer. (5 points)
