This paper reveals a characteristic of stable matchings in the college admissions problem and provides structural insights and a unified treatment for several results in this model, including the famous "Rural Hospital Theorem". We also show that the worst student determines the whole entering class.
This paper studies a many-to-one matching model, and shows that the set of envy-free matchings is a lattice. A Tarski operator on this lattice that can be interpreted as modeling vacancy chains, has the set of stable matchings as its fixed points.
Repugnant transactions are sometimes banned, but legal bans sometimes give rise to active black markets that are difficult if not impossible to extinguish. We explore a model in which the probability of extinguishing a black market depends on the extent to which its transactions are regarded as repugnant, as measured by the proportion of the population that disapproves of them, and the intensity of that repugnance, as measured by willingness to punish. Sufficiently repugnant markets can be extinguished with even mild punishments, while others are insufficiently repugnant for this, and become exponentially more difficult to extinguish the larger they become.
This paper studies a dynamic matching model in which a social planner creates team based game sessions for sequentially arriving players and seeks a balance between fairness and waiting times. We derive a closed-form optimal matching policy and show that as the team size grows and the market becomes more balanced, greedy policies become less appealing.
Competition between Streaming Platforms
This paper studies the matching between streamers and streaming platforms. The market is decentralized and has two features: first, platforms use a simple linear payment structure; second, there are externalities between streamers. We show that under a substitutability condition together with certain restriction on platform side externalities, a stable matching always exists. Furthermore, any job-hopping process such that streamers switch platforms seeking better terms eventually stabilizes, leaving stable matchings as the likely steady states of the market. We then study the game in which platforms select their payment rules and show that in a small market, although a Nash equilibrium always exists, there may not be a pure one. Finally we justify the payment scheme of platforms through a large market model in which platforms signing linear non-discriminatory contracts with streamers is an equilibrium outcome.
This was my undergraduate mathematics honor thesis, advised by Dr Florian Block. It studies Go endgames with tools in combinatorial game theory.
My math 191 project with Michael Landry, advised by Dr Daniel Cristofaro-Gardiner. We solve 2xn (except 2x31) and 3xn Domineering games by pure combinatorial arguments. The problem was first solved in the 1980s by Berlekamp. But he used advanced results from temperature theory, while we only use simple primitive arguments (a little bit tedious of course).
Another math 191 project with Michael Landry and Frank Yu, again advised by Dr Daniel Cristofaro-Gardiner. It is a note on how to do basic analysis on chess endgames with combinatorial game theory.
My first ever "paper" published in China, back to the days when I was a high school student. It introduces a method of constructing local inequalities based on function concavity, which is similar to the supporting hyperplanes in the proof of Jensen's inequality.
Another article I wrote when I was in high school. It describes a characteristic of equilateral triangles in the form of complex numbers. When applied properly, it can solve difficult geometry problems with ease.