Essays on matching and market design

This dissertation consists of three essays on matching and market design. The first essay, co-authored with Parag Pathak, analyzes the scope for manipulation in many-to-one matching markets under the student-optimal stable mechanism when the number of participants is large. Under some regularity conditions, we show that the fraction of participants that have incentives to misrepresent their preferences when others are truthful approaches zero as the market becomes large. With an additional technical condition, truthful reporting by every participant is an approximate equilibrium under the student. optimal stable mechanism in large markets. The results help explain the success of the student-optimal stable mechanism in large matching markets observed in practice.The second essay, co-authored with Mihai Manea, investigates the random assignment problem. In the random assignment problem, the probabilistic serial mechanism (Bogomolnaia and Moulin 2001) is ordinally efficient and envy-free, but not strategy-proof. However, we show that agents have incentives to state their ordinal preferences truthfully when the market is sufficiently large. Given a fixed set of object types and an agent with a fixed expected utility function over these objects, if the number of copies of each object type is sufficiently large, then truthful reporting of ordinal preferences is a weakly dominant strategy for the agent (for any set of other participating agents and their possible preferences) . The better efficiency and fairness properties of the probabilistic serial mechanism, together with the non-manipulability property we discover, support its implementation in many circumstances instead of the popular random serial dictatorship. The third essay investigates matching and price competition. A recent antitrust case against the National Resident Matching Program (NRMP) sparked discussion about the effect of a centralized matching on wages. Jeremy Bulow and Jonathan Levin (2006) investigate a matching market with price competition where each firm hires one worker and show that firm profits are higher and worker wages are lower in the equilibrium with the centralized matching mechanism than in any competitive equilibrium. We demonstrate these conclusions may not hold once firms can hire more than one worker and different firms hire different numbers of workers, as in most real-life matching markets including the NRMP.