abstract: In this paper, I study many-to-one matching markets in a dynamic framework with the following features: Matching is irreversible, participants exogenously join the market over time, each agent is restricted by a quota, and agents are perfectly patient. A form of strategic behavior in such markets emerges: The side with many slots can manipulate the subsequent matching market in their favor via earlier matchings. In such a setting, a natural question arises: Is it possible to analyze a dynamic many-to-one matching market as if it were either a static many-to-one or a dynamic one-to-one market? First, I provide sufficient conditions under which the answer is yes. Second, I show that if these conditions are not met, then the early matchings are "inferior" to the subsequent matchings. Lastly, I extend the model to allow agents on one side to endogenously decide when to join the market. Using this extension, I provide a rationale for the small amount of unraveling observed in the United States (US) medical residency matching market compared to the US college-admissions system. Micro Finance Institutions (MFIs) are designed to improve the welfare of the poor. Group lending with joint liability is the standard contract used by these institutions. Such a contract performs two roles: it affects the composition of the groups that form, and determines the properties of risk-sharing among their members. Even though the literature suggests that groups consist of members with similar characteristics, there is evidence also of groups with heterogeneous agents. The underlying reason is that the literature lacked the risk-sharing behavior of the agents within a group. This paper develops a model of group lending where agents form groups, obtain capital from the MFI, and share risks among themselves. First, I show that joint liability introduces inefficiency for risk-averse agents. Moreover, the composition of the groups is not always homogeneous once risk-sharing is on the table. / Dissertation/Thesis / Doctoral Dissertation Economics 2020

abstract: In the first chapter, I study the two-sided, dynamic matching problem that occurs in the United States (US) foster care system. In this market, foster parents and foster children can form reversible foster matches, which may disrupt, continue in a reversible state, or transition into permanency via adoption. I first present an empirical analysis that yields four new stylized facts related to match transitions of children in foster care and their exit through adoption. Thereafter, I develop a two-sided dynamic matching model with five key features: (a) children are heterogeneous (with and without a disability), (b) children must be foster matched before being adopted, (c) children search for parents while foster matched to another parent, (d) parents receive a smaller per-period payoff when adopting than fostering (capturing the presence of a financial penalty on adoption), and (e) matches differ in their quality. I use the model to derive conditions for the stylized facts to arise in equilibrium and carry out predictions regarding match quality. The main insight is that the intrinsic disadvantage (being less preferred by foster parents) faced by children with a disability exacerbates due to the penalty. Moreover, I show that foster parents in high-quality matches (relative to foster parents in low-quality matches) might have fewer incentives to adopt. In the second chapter, I study the Minnesota's 2015 Northstar Care Program which eliminated the adoption penalty (i.e., the decrease in fostering-based financial transfers associated with adoption) for children aged six and older, while maintaining it for children under age six. Using a differences-in-differences estimation strategy that controls for a rich set of covariates, I find that parents were responsive to the change in direct financial payments; the annual adoption rate of older foster children (aged six to eleven) increased by approximately 8 percentage points (24% at the mean) as a result of the program. I additionally find evidence of strategic adoption behavior as the adoption rate of younger children temporarily increased by 9 percentage points (23% at the mean) while the adoption rate of the oldest children (aged fifteen) temporarily decreased by 9 percentage points (65% at the mean) in the year prior to the program's implementation. / Dissertation/Thesis / Doctoral Dissertation Economics 2019

Allocation of objects or resources to competing agents is a ubiquitous problem in the real world. For example, a federal government may wish to allocate different types of spectrum licenses to telecom service providers; a search engine has to assign different sponsored slots to the ads of advertisers; etc. The agents involved in such situations have private preferences over the allocations. The agents, being strategic, may manipulate the allocation procedure to get a favourable allocation. If the objects to be allocated are heterogeneous (rather than homogeneous), the problem becomes quite complex. The allocation problem becomes even more formidable in the presence of a dynamic supply and/or demand. This doctoral work is motivated by such problems involving strategic agents, heterogeneous objects, and dynamic supply and/or demand. In this thesis, we model such problems in a standard game theoretic setting and use mechanism design to propose novel solutions to the problems. We extend the current state-of-the-art in a non-trivial way by solving the following problems: Optimal combinatorial auctions with single minded bidders, generalizing the existing methods to take into account multiple units of heterogeneous objects Multi-armed bandit mechanisms for sponsored search auctions with multiple slots, generalizing the current methods that only consider a single slot. Strategyproof redistribution mechanisms for heterogeneous objects, expanding the scope of the current state of practice beyond homogeneous objects Online allocation mechanisms without money for one-sided and two-sided matching markets, extending the existing methods for static settings.