3. Consider an assignment problem (e.g., allocating houses to agents). Agents' preferences are given as follows: P(a1) : h3 > h5 > h > h4 > h2; P(a2) h5h1 > h3 > h > h4; P(a3) h4 h > h3 > h > h5; P(a4) h5 > h1> h2 > h3 > h4; P(as) h4h2 h > h5 > h3. (a) Assume private endowment. That is, agent a; owns house hi (for i = 1, . . ., 5). i. Find the outcome of TTC algorithm. ii. Explain shortly ( < 100 words) that the above outcome is in the core. Your explanation should take into account the initial endowment. (b) Now, assume that only a2, 3, and 5 own h2, h3, and h5, respectively. The other two houses are public endowment. Find the outcome of YRMH-IGYT algorithm, when agents are initially ordered as a > a > A3 > A4 > A5.