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

An experimental study on the incentives of the probabilistic serial mechanism

We report an experiment on the Probabilistic Serial (PS) mechanism for allocating indivisible goods. The PS mechanism, a recently discovered alternative to the widely used Random Serial Dictatorship mechanism, has attractive fairness and efficiency properties if people report their preferences truthfully. However, the mechanism is not strategy-proof, so participants may not truthfully report their preferences. We investigate misreporting in a set of simple applications of the PS mechanism. We confront subjects with situations in which the theory suggests that there is an incentive or no incentive to misreport. We find little misreporting in situations where misreporting is a Nash equilibrium. However, we also find a significant degree of misreporting in situations where there is actually no benefit to doing so. These findings suggest that the PS mechanism may have problems in terms of truthful elicitation

House Allocation with Overlapping Agents: A Dynamic Mechanism Design Approach

Many real-life applications of house allocation problems are dynamic. For example, in the case of on-campus housing for college students, each year freshmen apply to move in and graduating seniors leave. Each student stays on campus for a few years only. A student is a "newcomer" in the beginning and then becomes an "existing tenant". Motivated by this observation, we introduce a model of house allocation with overlapping agents. 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 simple dynamic mechanism that is strategy-proof and Pareto efficient.house allocation, overlapping agents, dynamic mechanism, top trading cycles, serial dictatorship

Second-best incentive compatible allocation rules for multiple-type indivisible objects

We consider the problem of allocating several types of indivisible goods when preferences are separable and monetary transfers are not allowed. Our finding is that the coordinatewise application of strategy-proof and non-wasteful rules yields a strategy-proof rule with the following efficiency property: no strategy-proof rule Pareto-dominates the rule. Such rules are abundant as they include the coordinate-wise use of the two well-known priority-based rules of the top trading cycles (TTC) and the deferred acceptance (DA). Moreover, our result supports the current practice in Market Design that separately treats each type of market for its design. (author's abstract