Game Theory in the High School Application Process
The high school application process for students in New York City is a tough and challenging process, with approximately 75,000 students trying to be placed in one of the 426 public high schools. In this school admissions matching market, finding a perfect match is a nearly impossible task, because with so many students and a high overlap of preferred schools in a list of 5, the possibility of receiving their desired choice would be incredibly low due to the presence of constricted sets, which we have discussed in class. According to the data presented, only some would be matched with one of their preferred choices, the higher performing students would have the freedom of choice from multiple schools, while students coming from lower-income families with less resources and opportunities would not even get a match at all. This would be an example of a congested matching market that perpetuates inequality between social classes.
To address this problem and seek for a better solution, game theory came into play. Professors Atila Abdulkadiroglu from Duke, Parag Pathak from MIT, and Alvin E. Roth from Stanford, modelled a new admissions system based on the famous stable marriage problem proved by David Gale and Lloyd Shapley mentioned in this course. The stable marriage problem showed that there can always be stable matching given the preferences of both parties, stable meaning that each player’s preference is optimised. According to the algorithm of the stable marriage problem, the “deferred acceptance algorithm”, the three professors created a version targeting students and schools. The students provide a list their preferred 12 schools in order, and the schools provide a list of students that they would like to admit, just like how both the men and women in the stable marriage problem list out their preferences. The algorithm allows students to first apply to their first choice school, which the school then either accepts or rejects. If the student is rejected from their first choice, the algorithm then matches the student to their second-choice school for a new chance of applying. The process continues until the student is matched with a school that accepts them. This way, every student is guaranteed a match that is based on mutuality, similar to the matches created in the stable marriage problem, where both party’s preferences are optimised.
With the implementation of game theory in matching markets, although it was still impossible to achieve a perfect matching, the number of unmatched students increased drastically because the deferred acceptance algorithm guaranteed a mutual matching. However, algorithms alone are not enough to solve the problem of high school admissions. The allocation issue is highly dependent on social stratification, the inequality of access to resources, and the lack of support for low-income populations. Thus, the application of game theory in the high school admissions process led to significant progress in increasing the success of matches. What is left is to address is the disproportionate imbalance of choice success rate between the low-performing and high-performing students.