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Use of Game Theory to Improve High School and University Application Process

 

A New York Times article by Tracy Tullis examines how game theory helped improve New York City’s high school application process (Link 1). While the article focuses on the application to the high school application process, the theories introduced are also applicable to other admission processes such as for college. Moreover, it is interesting to view the problem in terms of no only game theory but also matching markets.

Before the improvements, the NYC high school allocation process involved middle schoolers submitting five choices of high schools listed in order of priority. The system paired some, usually high-performing ones, with more than one of their choices while pairing almost half, many from disadvantaged backgrounds, with a school not among their choices at all. The strategy that was computed was far from a perfect match. The system was resigned in 2003 based on the deferred acceptance algorithm, for which Professor Alvin E. Roth of Stanford won the 2012 Nobel Memorial Prize in Economic Science. The new system requires students to submit a list of schools in order of preference and requires schools to submit a list of students ranked in preference. How the algorithm works is that in every round of matching, each student who was rejected or not matched in the previous round is paired with his or her next top choice school. Each school then considers the set of students that has been paired with it in previous rounds up until the current round. Lastly, the school accepts those ranked the highest out of the whole pool up until then and reject the others. The cycle repeats until all students have been matched. While “school” is used as the subject in these actions, the whole process is in fact automated with computers. As long as students and the schools submit a truthful ranking of their choices, aka “true preference order,” the algorithm will ensure that the most optimal matches are assigned. After the redesign, the number of unmatched students decreased from 31,000 in the previous year to about 3000.

As a Quora post also about game theory on application processes (Link 2) commented, the deferred acceptance algorithm is Pareto efficient, which as we have learned in class means that there is no other choice of strategies in which any students or schools receive the same payoff, and at least one student or school makes a better match. The computed strategy is also considered stable as no school or student has an incentive to deviate from their designated match for a match that makes them better off. Tying the discussion of stability back to our study of equilibrium in class, the algorithm computes a Nash Equilibrium strategy of the system since all students and schools are playing their best response to that of each other.

In comparison to the NYC school application process, the college application process differs in that students and colleges have no knowledge of their rankings in the opposing party’s list. Moreover, students are not limited to applying to a set number of colleges. Nonetheless, the application process can be modeled with students and colleges as the players, the matching of students to colleges as strategies, and how satisfied students and colleges are with their matches as the payoffs. Most universities across the country have experienced a trend of increasing numbers of applicants and decreasing admission rates in recent years. These stats only prompt more high school seniors to apply to a larger number of schools in hope of increasing their personal chances. This situation in fact epitomizes the arm race situation discussed in class.

Other than game theory, the college application process can be related to the topic of matching markets. The students are modeled as the buyers and the schools are modeled as the sellers. At first glance, it appears that matching market is not a suitable model for this situation because the sellers are also particular about who they sell to. However, the colleges’ tuition and choice of admitted student can be thought of as the buyer’s price for its goods. Just like typical sellers, colleges look at the market and assess how much demand the buyers (students) have for the goods (education) they offer. Colleges can then lower or raise the price of its goods through amount of tuition as well as the students that they make acceptance offers to. For instance, raising the price too high, such as having high tuition and making offers to much too high achieving students, risk leading to a low number of deals (low yield rate). In contrast, lowering the price too much leads to a lower payoff (less tuition and lower-achieving students). A perfect match and market clearing prices are not applicable or possible in this situation, as there is an unequal number of buyers and sellers in the market. Nonetheless, optimization of application processes seeks to make matches as close to perfect matches as possible.

Link 1: https://www.quora.com/How-can-game-theory-improve-high-school-universities-application-process

Link 2: https://www.nytimes.com/2014/12/07/nyregion/how-game-theory-helped-improve-new-york-city-high-school-application-process.html

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