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 (SD) and top trading cycles (TTC), both of which are based on an ordering of agents and give an agent with higher order an opportunity to obtain a better house. We show that for SD mechanisms, the ordering that favors existing tenants is better than the one that favors newcomers in terms of Pareto efficiency. Meanwhile, this result holds for TTC mechanisms under time-invariant preferences in terms of Pareto efficiency and strategy-proofness. We provide another dynamic mechanism that is strategy-proof and Pareto efficient.