Essays on Matching Markets

Abstract

The thesis "Essays on Matching Markets" contributes to the theory and applications of matching theory.<br /> The first chapter analyzes the German university admissions system and proposes an alternative admissions procedure that outperforms the currently used mechanism. In particular, the new mechanism provides strong (i.e. dominant strategy) incentives for applicants to reveal their true preferences and achieves a notion of stability that is adapted to the German system.<br /> In the second chapter we analyze the school choice problem with indifferences in priority orders. In this context, stability (with respect to student preferences and school priorities) can be understood as a fairness criterion which ensures that no student ever envies another student for a school at which she has higher priority. Since school seats are objects to be allocated among students, it is important to ensure that a constrained efficient allocation is selected, i.e. an allocation that is stable and not (Pareto-) dominated by any other stable matching. A counterexample of Erdil and Ergin (American Economic Review, 2008) shows that there may not exist a non-manipulable and constrained efficient mechanism. We consider the case where students either all have the same priority or all have distinct priorities for a given school. For this important special case we investigate whether the negative result of Erdil and Ergin is the rule or an exception and derive sufficient conditions for the existence of a constrained efficient and (dominant strategy) incentive compatible mechanism. The proof is constructive and shows how preferences of students can (sometimes) be used to prevent any welfare loss from tie-breaking decisions.<br /> The third chapter deals with a more general matching model recently introduced by Ostrovsky (American Economic Review, 2008). For this model we analyze the relation between Ostrovsky's chain stability concept, efficiency, and several competing stability concepts. We characterize the largest class of matching models for which chain stable outcomes are guaranteed to be stable and robust to all possible coalitional deviations. Furthermore, we provide two rationales, one based on efficiency and the other based on robustness considerations, for chain stability in the general supply chain model.