Q1 Deferred Acceptance Algorithm Consider the example of the deferred acceptance algorithm from the class. The set of men consists of M = {Putin, Iron Man, Darth Vader and Trump} and the set of women included W = { Hermione, Leia, Melania and Oprah}. The DA considered in class progressed as follows: Round 1: Putin and Iron Man propose to Leia. Darth Vader and Trump propose to Oprah. Leia accepts Putin and rejects Iron Man. Oprah accepts Darth Vader and rejects Trump. Round 2: Iron Man proposes to Oprah, and Trump proposes to Hermione. Oprah rejects Dart Vader and accepts Iron Man. Hermione accepts Trump. Round 3: Darth Vader proposes to Hermione. Hermione rejects Trump and accepts Darth Vader. Round 4: Trump proposes to Leia. Leia rejects Trump. Round 5: Trump proposes to Melania. Melania accepts Trump. Hint: you might want to review the class slides with this example. Answer the following questions: (a) To the extent possible, reconstruct the rank lists that participants have used. (b) Given reconstructed preferences, will you be able to run woman-proposing version of DA? Why or why not? (c) Suppose that Darth Vader would have ranked Melania higher than Hermione, but still lower than Oprah. Would the man-proposing DA have resulted in a different match? Why or why not? Does you answer depend on whether Melania finds Darth Vader acceptable? (d) Suppose that Trump would have ranked Melania higher than Hermione. Would the man- proposing DA have resulted in a different match? Why or why not