|Abstract:||Matching markets are common methods to allocate resources around the world.
There are two kinds of matching market: centralized matching market and decentralized matching market.
In a centralized matching market, there is a clearing house that functions to collect information from market participants and uses the information to determine the allocation among the participants.
In a decentralized matching market,
market participants contact one another and possibly exchange information, and the allocation is
determined among the participants based on their agreement.
In my thesis, I study the matching markets that are two-sided.
In a two-sided matching market, participants are separated into two groups.
For example, men and women, schools and students, and so on.
Such a market is first studied by Gale and Shapley (1962).
They study matching markets between men and women
and between colleges and students.
Consider the simples matching problem: the marriage problem, the problem of matching between men and women.
Each of them has a preference over the agents on the opposite side and the option of remaining single.
A central question is: does a matching that is individual rational and no pair of agents from different
sides who are not matched together but rather be together exist? (Such a matching is referred as a stable matching.)
Gale and Shapley (1962) show that the answer is affirmative with the introduction of the deferred acceptance algorithm.
Since Gale and Shpaley (1962), the concept of stability and the application of deferred acceptance
algorithm are widely used in the literature of two-sided matching.
My thesis consists of four individual papers.
Chapter 1, with the title "When is the Boston Mechanism Dominance-Solvable?", Chapter 2, with the
title "Undominated Strategies and the Boston Mechanism", and Chapter 3, with the
title "Promoting Diversity of Talents: A Market Design Approach", are my own work.
In these three chapters, I study the matching problems between schools and students.
Chapter 4, with the title "Platform Markets and Matching with Contracts", is a joint work of Juan Fung and I.
In this chapter, we propose a model to study platform markets.