W 2 â m 1 w 3 â m 1 w 4 â m 1 w 1 m 3 â w 1 m 4

Info icon This preview shows pages 2–3. Sign up to view the full content.

View Full Document Right Arrow Icon
w 2 Â m 1 w 3 Â m 1 w 4 Â m 1 w 1 , m 3 Â w 1 m 4 Â w 1 m 1 Â w 1 m 2 w 2 Â m 2 w 3 Â m 2 w 4 Â m 2 w 1 , m 4 Â w 2 m 1 Â w 2 m 2 Â w 2 m 3 w 2 Â m 3 w 3 Â m 3 w 4 Â m 3 w 1 , m 1 Â w 3 m 2 Â w 3 m 3 Â w 3 m 4 w 4 Â m 4 w 1 Â m 4 w 2 Â m 4 w 3 , m 2 Â w 4 m 3 Â w 4 m 4 Â w 4 m 1 (a) What is the W-optimal stable matching? De fi ne W-optimal sta- ble matching by words or using mathematical notations. (b) Find the W-optimal stable matching. Explain how you derived it. (c) Find the M-optimal stable matching. Explain how you derived it. 2
Image of page 2

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
(d) Suppose that Women-proposing DAA is used. Show that every man can misrepresent his preference (including the ranking of staying alone) to generate the M-optimal stable matching, assum- ing that everyone else reveals his or her true preference honestly. (e) Suppose that w 3 ’s preference is given by m 1 w 3 m 2 Â w 3 m 3 Â w 3 m 4 instead, i.e. w 3 is indi ff erent between m 1 and m 2 . We apply DAA by introducing an arti fi cial tie-breaking. Show that, given some tie-breaking rule, DAA leads to an allocation that is not W-optimal . 3
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern