Due: Wednesday, January 15th in class.

Remember to take a look at the grading guidelines.

Reading assignment: Kleinberg-Tardos, Chapters 1-2.

In solving the problem sets, you are allowed to collaborate with fellow students taking the class, but remember that you are required to write up the solutions by yourself. If you do collaborate in any way, you must acknowledge, for each problem, the people you worked with on that problem.

The problems have been carefully chosen for their pedagogical value, and hence might be similar to those given in past offerings of this course at UW, or similar to other courses at other schools.  Using any pre-existing solutions from these sources, for from the web, constitutes a violation of the academic integrity you are expected to exemplify, and is strictly prohibited.

Most of the problems only require one or two key ideas for their solution. It will help you a lot to spell out these main ideas so that you can get most of the credit for a problem even if you err on the finer details. A final piece of advice:  Start working on the problem sets early!  Don't wait until the day (or few days) before they're due.

Problems

  1. Kleinberg and Tardos, Chapter 1, Problem 5, pages 24-25
  2. Kleinberg and Tardos, Chapter 1, Problem 7, pages 26-27  [HINT: Try to set up a stable matching problem that will solve this problem]
  3. Kleinberg and Tardos, Chapter 2, Problem 4, pages 67-68
  4. Kleinberg and Tardos, Chapter 2, Problem 6, page 68

Extra credit

  1. Kleinberg and Tardos, Chapter 1, Problem 8, pages 27-28

  2. (a) Show that it's possible for a woman to cheat the Gale-Shapley stable matching algorithm by lying about her preferences. In other words, show that there are situations where a woman could get a better partner by giving a misleading preference list to the algorithm.

    (b) Prove that, even if a man knows all the other preferences, he cannot do any better for himself by lying about his true preferences.