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.