Essays on Market Design and Auction Theory

This dissertation studies market design and auction theory. Chapter 1 studies the impact of school choice on segregation. It shows that the popular school choice mechanisms lead to substantially different school and residential segregation, an important and overlooked aspect of choosing among school choice mechanisms. We show that open enrollment policy in public school choice program can decrease diversity of individual schools and increase segregation depending on which student allocation mechanism is used. Without open enrollment, we study the model of location choice and show that segregation is mainly associated with income. In comparing mechanisms, we show that Boston mechanism fosters segregation more than the deferred acceptance. With open enrollment, the difference between BM and DA becomes more drastic. We show that BM can actually intensify segregation when open enrollment policy is adopted, while DA is more resilient to segregation. The deferred acceptance with multi tie breaking creates maximally diverse schools. Chapter 2 considers conventional auctions when the seller can design bid spaces. Any symmetric equilibrium in a second price auction with bid spaces can be replicated with an equilibrium in a first price auction with bid spaces, but the converse doesn't hold. First price auctions with designed bid spaces revenue dominates second price auction with designed bid spaces, and well-designed first price auction is an optimal selling mechanism. Chapter 3 studies one-to-one matching environment without transfer in the presence of incomplete information on one-side. The existing notions of stability under incomplete information are studied and two alternatives are proposed. Weak Bayesian stability requires that the beliefs of the agents are dervided from a common prior via Bayes' rule and are internally consistent with the presumption that the given matching is stable. Strong Bayesian stability refines weak Bayesian stability by requiring the beliefs of agents are also externally consistent in the sense that the beliefs are narrowed down only when there is a valid reason