Game Theory and New York City’s High School Admissions Process
Link: https://www.nytimes.com/2014/12/07/nyregion/how-game-theory-helped-improve-new-york-city-high-school-application-process.html
The article written for the New York Times by Tracy Tullis explores the dynamic between high school applicants and acceptances through the lens of game theory. The inefficiencies of the high school applications process are highlighted, where in the 1990’s students would submit a list of the top five schools they wanted to attend. While the top-performing students would receive offers from multiple schools and get to decide on which option they wanted, many lower-performing students received no matches at all, waiting the entire summer and then attending a school that wasn’t even on their list. This happened to almost half of the eighth-graders living in the city, resulting in the need for an improved sorting model for thousands of students.
The three economists who designed the new matchmaking system were Atila Abdulkadiroglu, Parag Pathak, and Alvin Roth, who implemented a deferred acceptance algorithm based on mutuality. The principle from game theory that they focused on was stability, which, as mentioned in the article, “means that every player’s preferences are optimized.” In other words, students make a list of their preferred schools in order, schools make a list of students they want, and both are paired by a computer in such a way that the student gets their highest-ranked school that also wants them. These pairings are tentative until the end of all rounds, when they are finalized. This is crucial, because if a school tentatively matches with a student in earlier rounds, it can reject them in later rounds if it finds a student higher on its list. This ensures the matches are optimized for as many people as possible. By the end of the rounds and with the help of game theory, most students are matched to one of the choices on their lists and those who aren’t are assigned in additional rounds. The analogy used in the article was the stable marriage problem, where a proposed match is accepted or rejected tentatively until the end of all the rounds.
In using concepts from game theory, the number of unmatched students in New York City went from 31,000 to 3,000, a drastic decrease and clear improvement in the admissions process. However, the problem of resource allocation is still apparent, as there aren’t enough good schools for every student, especially those from low-income backgrounds. With the algorithm, almost half of all students were assigned their first choice and a third were assigned to their second or third choices. It is important to note, however, that many of the top choices are matched simply because lower-achieving students rank lower-achieving schools as their top choices, and the same is true for higher-achieving students and higher-achieving schools. In addition, not all assumptions made in game theory hold true in real life. Many students will apply to schools close to home, even if the schools are lower-achieving. Different factors also affect the high schools that students apply to, including social, economic, and political pressure from both family and friends. While game theory certainly helped with the process, there is still room for improvements that are rooted both in the students’ background and intrinsically in the number of resources available. Perhaps through further research and algorithm experimentation built upon concepts in game theory, the high school applications process in the city can be streamlined further and more students can attend the school of their choice.