1. cs234r Markets for Networks and Crowds B RENDAN L UCIER, M ICROSOFT R ESEARCH NE N ICOLE I MMORLICA, M ICROSOFT R ESEARCH NE

2. Lecture 2: Eduardo Azevedo and Jacob Leshno. A supply and demand framework for two-sided matching, Journal of Political Economy, forthcoming. Preliminary version in ACM Conference on Economics and Computation, 2011.

3. Thresholds: Informal main idea: Stable matchings correspond to market-clearing admission thresholds. Colleges accept students that pass threshold. Students select their favorite college among those that accept them.

4. Model:

6. Outcome:

7. Stability:

8. Market-Clearing:

10. Supply and Demand:

11. Example:

12. Deferred-Acceptance:

13. Step 1: a)Students apply to favorite college that has not yet rejected them b)Colleges reject students over capacity.

14. Step 2: a)Students apply to favorite college that has not yet rejected them b)Colleges reject students over capacity.

15. Limit:

16. INFORMAL Discussion: Uniqueness: If system of market-clearing equations has unique solution, then there is a unique stable match. if set of students “rich enough” if schools “over-demanded” Convergence: Continuum stable matching is limit of sequence of finite economy stable matchings (where distribution/capacities converge).

17. INFORMAL Discussion: School Improvement: Azevedo-Leshno show schools have stronger incentives to invest in programs that attract high-quality students. Constructing Menus: Ashlagi-Shi use this correspondence to design school preferences and “menu of options” for students in Boston school choice that maximizes welfare.