Essays on Dynamic Matching Markets

The static matching models have been applied to real-life markets such as hospital intern markets, school choice for public schools, kidney exchange for patients, and on-campus housing for college students. However, these markets inherently involve dynamic aspects. This dissertation introduces dynamic frameworks into representative matching models - two-sided matching markets and house allocation problems, and obtained policy implications that cannot be captured by static models.The first two essays are devoted to two-sided matching models in which two-sided matching interactions occur repeatedly over time, such as the British hospital intern markets. In the first essay, we propose a concept of credible group stability and show that implementing a men-optimal stable matching in each period is credibly group-stable. The result holds for a women-optimal stable matching. Moreover, a sufficient condition for Pareto efficiency is given for finitely repeated markets. In the second essay, we examine another notion of one-shot group stability and prove its existence. Moreover, we investigate to what extent we can achieve coordination across time in the infinite horizon by using the one-shot group stability.The third essay focuses on the house allocation problem - the problem of assigning indivisible goods, called ``houses," to agents without monetary transfers. We introduce an overlapping structure of agents into the problem. This is motivated by the following: In the case of on-campus housing for college students, each year freshmen move in and graduating seniors leave. Each students stays on campus for a few years only. In terms of dynamic mechanism design, we examine two representative static mechanisms of serial dictatorship.