Engineering the Allocation of Public Resources

Unit 1: Foundations

Session 1: Efficiency
- Pareto Efficiency; Rank Efficiency; Serial Dictatorship; First Choices First
Session 2: Incentives
- Truthful; Individually Rational; the Core; Board Game “Math Trades”
Session 3: TTC + Fairness
- Top Trading Cycles; Random Mechanism; Symmetry
Session 4: A Striking Equivalence
- Random Serial Dictatorship; Top Trading Cycles from Random Endowments

Unit 2: School Choice and Residency Matching

Session 5: Intro to School Choice
- First Choices First (Boston); Generalized Top Trading Cycles; Justified Envy; Respecting Priorities
Session 6: The Deferred Acceptance Algorithm
- School/Student Proposing Deferred Acceptance; Lone Wolf Theorem; Student Optimal Stable Match
Session 7: Intro to Residency Matching
- Truthfulness of Deferred Acceptance; Unraveling; Stability
Session 8: Matching with Couples
- Non-Existence of Stable Matching; Small Core;
Session 9: Tiebreaking
- Weak Stability; Strong Stability; Single Tiebreaking; Multiple Tiebreaking
Session 10: University Admissions

Unit 3: Affirmative Action

Session 11: Maximum Quotas
- Maximum Quota; Priority Domination; Hierarchy; Diversity Visa Lottery;
Session 12: Minimum Quotas
- Minimum Quota; Mechinot Gap Year Matching
Session 13: Chilean Constitutional Assembly Case Study
Session 14: Intro To Reserves
- Minimum Guarantee; Over and Above; Sequential Lotteries; H1B Visa Lottery
Session 15: Affirmative Action in India
- Vertical Reservations; Horizontal Reservations; Overlapping Reservations
Session 16: Affirmative Action in Brazil
Session 17: Matching with Complex Preferences
- Substitutability; Law of Aggregate Demand; Irrelevance of Rejected Contracts; Generalized Deferred Acceptance (Cumulative Offers)
Session 18: Matching with Contracts
- Kelso-Crawford; Cadet Branch Matching; University Admission with Financial Aid

Unit 4: Organ Allocation

Unit 5: Affordable Housing