This thesis consists of two essays on education market design. Chapter 1, “Education Market in the Presence of Peer Effects: Theory and Evidence From South Korea” is a joint work with Sam Il Myoung Hwang. In this paper we evaluate alternative market designs in the presence of peer effect considerations in school choice. Schools can differentiate by peer composition among other characteristics. Different rules public schools are subject to compared to elite or private schools have been heavily debated because of their effects on student distribution. In many countries former group admit students earlier than the latter, which we call Sequential Admissions (SA). Furthermore, the former group can use academic criteria in admissions unlike the latter. We study the effect of these admission aspects on welfare and distribution. Our analysis has important distinguishing features. First, it includes private schools as well as public schools, whereas previous studies on admission rules focused on centralized public school allocation. Second, students can have preferences for peer composition at schools. This is an important factor that can determine sorting behavior which is not carefully studied before. First we theoretically study equilibria of the admission games complicated by the peer effects. Then we estimate a structural model using detailed high school applications data from Seoul to run counterfactual simulations. We show that SA can approximate centralized admission schemes well. This is important since complete centralization is known to increase welfare but hard to implement in many cases. Moreover analysis of SA is informative on the controversial “exploding offers” in labor markets. Regarding admission criteria, we show that use of academic criteria in a subset of schools increases the desirability of these schools. The reason is that high performing students want to coordinate to study together and academic screening provides this. This suggest that, school choice is also a coordination game, not just an object allocation problem. Chapter 2, “The Role of Outside Options under Boston Mechanism” studies ex ante welfare from centralized public school allocation for students who cannot go to private schools when there are others who have such option. I show that when a private school is preferred to only the last option, students prefer Boston Mechanism (BM) to Deferred Acceptance (DA). Analyzing the case of desirable private schools in a model with three public schools, I demonstrate that students who are marginal in the decision of which school to report as top choice are better off under DA compared to BM; whereas inframarginal students are better off under BM. I show that a distribution of preferences with full support guarantees the existence of students who are better off under BM compared to DA. Assuming uniform distribution of preferences allows one to find the fraction of students who are better off under BM compared to DA. Analysis of the effect of private school entry on the welfare of students who cannot access private schools demonstrates that under mild conditions either there are students who are strictly better off after the entry or welfare of none of the students change.