Thesis advisor: Utku Unver / My doctoral research focuses on the matching theory and its market design application. Specifically, I work on matching with property rights, where property rights not only mean the ownership, but also refer to the ability to determine how the good is used. In the matching with property rights model, an agent who owns a resource can claim how her resource is offered, depending on what she gets from the system. For example, in a housing exchange for vacation, an agent who gets a house with a car will offer her house also with a car. However, if she is assigned only a house without a car, she might refuse to offer a car. This restriction can be thought as a matching with externality, as someone's consuming my resource in certain way affects my utility. With property rights present, it is not clear how we can achieve a desirable outcome while satisfying the rights. I am currently pursuing two main lines of research in this topic that constitute the two chapters dissertation. In Matching with Property Rights: an Application to a Parking Space Assignment Problem, I introduce parking in urban areas as a matching problem. First, I model the street-parking market as a strategic game and show that the set of Nash equilibrium outcomes is equivalent to the set of stable allocations. However, it is not reasonable to expect drivers to reach a Nash equilibrium in the decentralized system due to lack of information and coordination failure. Therefore, I suggest a centralized mechanism that would enable a parking authority to assign available spaces to drivers in a stable way. The model incorporates resident parking spaces, such that visitors could access vacant resident spaces. To use the resident parking spaces, the system needs to protect exclusive property rights over their parking spaces. I show that, however, there is no mechanism that is stable and protects residents' rights. To resolve this issue, I introduce a new concept, a claim contract, and suggest a mechanism that protects property rights, is strategy proof for the drivers, and approximates a stable matching. Besides its market-design focus, this paper handles both priority-based and property right-based assignment, which considered separately in the matching theory literature. In Housing Market with Contracts, I study matching with property rights problem in the housing market framework. To introduce property rights in housing market, I assume the house can be offered in two contractual terms. Property rights requires that when an agent gets a house in a certain term, her house should also be offered as the same term. Moreover, when every agent owns a house, property rights reduces to an equal-term matching. After defining efficiency and core in equal-term domain, I show that, in a housing market with contracts problem, core may be empty. However, there always exists an efficient, individually rational, and equal-term matching in every housing market with contracts problem. Then I present a mechanism that always produces an efficient, individually rational, and equal-term matching. This is the first attempt to model a matching with contract in a exchange economy. / Thesis (PhD) — Boston College, 2018. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Economics.