Essays in Matching

Abstract

In this dissertation, I study the properties of and propose the use of a family of random mechanisms for a large class of problems where agents need to be matched to objects or to each other without the use of monetary transfers. In the first chapter, I study the problem of kidney exchange under strict ordinal preferences and with constraints on the length of the trading cycles. The requirement of individual rationality in this setting incentivizes patient-donor pairs who are compatible with each other to participate in the kidney exchange, thus increasing the match rate for incompatible pairs. I show that deterministic mechanisms have poor properties in this environment. Instead, I explicit..