Matching market design : from theory to practice - Li, Mengling (2015)
This thesis examines efficiency and fairness in matching markets. We first study a generalized many-to-many matching problem with ties. A natural solution concept is Pareto stability, which ensures both stability and Pareto efficiency. We show that a Pareto stable matching always exists by developing an efficient algorithm to compute one. Next, for a practical problem where one side of the market has homogeneous preferences, we propose two new competing Pareto stable matching mechanisms. In the application of course allocation problem, we run simulations with unique course matching data which show that the Pareto stable matching mechanisms can significantly improve the overall efficiency and welfare of the students. Finally, we consider the generalized roommates problem with N students to be assigned to M rooms. Students may have weak preferences and rooms can have different capacities. We show that a Pareto efficient assignment always exits by introducing efficient algorithms to compute such assignments.