Many public school choice programs use centralized mechanisms to match students with schools in absence of market-clearing prices. Among them, the Boston mechanism is one of the most widely used. It is well-known that truth-telling may not be optimal under the Boston mechanism, which raises the concern that the mechanism may create a disadvantage to parents who do not strategize or do not. strategize well. Using a data set from Beijing, the first chapter investigates parents' strategic behaviors under the Boston mechanism and its welfare implications. School choice is modeled as a simultaneous game with parents' preferences being private information. I derive restrictions on parents' behavior under various assumptions on their ability to predict others' behavior, and the model is estimated using simulated maximum likelihood. The results suggest that parents' sophistication is heterogeneous; when parents have a greater incentive to behave strategically, they pay more attention to uncertainty and strategize better. There is no robust evidence that wealthier and/or more educated parents strategize better. If the Boston mechanism is replaced by the Deferred-Acceptance mechanism under which truth-telling is always optimal, the majority of the sophisticated parents who always play a best response are worse off. This kind of reform benefits half of the naive parents who are always truth-telling under the Boston mechanism, while it also hurts about 20% of them. The second paper studies the problem of matching students (agents) with schools (objects) in a more general setting. In the case of one-sided matching where schools have no preferences/priorities over students, Hylland and Zeckhauser (1979) proposes the Competitive Equilibrium from Equal Incomes (CEEI) mechanism which elicits students' cardinal preferences and creates a pseudo-market. The mechanism produces random assignments that are envy-free and ex ante efficient if students are truth-telling. Although it is not strategy-proof in general, I show that the incentive to deviate from truth-telling by any student vanishes when the market becomes large, given that all other students are telling the truth. The mechanism is then generalized to the case of school choice where each school has a weak priority ordering over students. The asymptotic incentive properties still hold, while its envy-freeness and ex ante efficiency are satisfied under the constraints of schools' priorities. The CEEI mechanism is also compared with the Boston mechanism which can be viewed as an approximation of the decentralized CEEI mechanism. Under certain conditions, the two mechanisms produce the same assignment. Moreover, I provide several practical procedures to use the Boston mechanism to achieve/approximate the CEEI random assignment and resolve it into deterministic assignments. Compared with other popular mechanisms, such as the random priority, probabilistic serial, deferred-acceptance, and top-trading-cycles mechanisms, the CEEI mechanism has more desirable features in general. The third chapter investigates if shared housing is a way to reduce homelessness. Most single adults share housing with other adults, and living alone is considerably more expensive than living with someone else. Yet policies that discourage shared housing for formerly homeless people or people at risk of becoming homeless are common, and those that encourage it are rare. This would be understandable if such housing adversely affected its users in some way. This chapter asks whether shared housing produces adverse effects. The provisional answer is no. For the most part, whether a person lives alone or shares housing seems to make no difference to the outcomes we studied although shared housing is associated with reduced psychotic symptomology. The chapter uses data from ACCESS, a 5-year, 18-site demonstration project with over 6,000 formerly homeless individuals as participants. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]