How can we use a lens of Game Theory to analyze whether test-optional college admissions is really the best way for colleges to get to know the thousands of students that they know.

136 0

Hi everyone! I’m Ruhaan, senior from Bloomfield Hills, Michigan. Over the next 5-10 minutes that you spend on my page, we will take a deep dive into the college admissions process. Specifically, we will look at the efficacy of test optional policies. Over the last 3-4 months, I have been exploring game theory here at GOA. In this project, I hope to apply what I’ve learned. Hope you enjoy!


Importance of the topic:

For the 2021, the common app received 6,060,037 applications. This number represents a stark 10-11% increase over the applying class last year. This means that, even in a pandemic, more kids than ever are applying to college. As I will describe later on this page, with many test centers closed, lots of colleges elected to offer a test optional approach to admissions.


College Admissions Trends (07′-17′)

Just based on this graph alone, we see that more kids than ever are applying to college!

Statement of the problem: 

Let’s be honest here: from the outside, test optional doesn’t seem like such a bad idea, right? If kids were unable to take tests, it makes sense to make those tests optional to “level the playing field,” as many colleges describe on their admissions pages. The reality is that by offering a test optional approach to college admissions, admissions officers are making college acceptances even more subjective than they already are. And with the removal of a vital piece of information about applicants, it really makes us wonder, how much are colleges really getting to know their applicants…

For the past 8 or so months, I have been working on and refining my college applications. This is a process that a majority of seniors go through every single year around this time. As I have been going through the process, there have been things that I have noticed that are potentially eye opening to the rest of the public. One of the many questions that I had to answer this year was whether or not to submit test scores to colleges. With the onset of the pandemic forcing multiple testing centers to shut down, many students were unable to sit in for a standardized test (SAT or ACT). Knowing this, almost every major college in the US elected to inherit a test optional policy, where students do not need to submit test scores with their application. As with any change in the college admissions process, this move to a test free application was bound to make changes to the way kids apply to colleges, and inevitably, it was going to help some specific groups of students more than others. 

Empathy Interviews:

To look more into the background of the problem here, I interviewed different parents of kids applying to college this year under a test optional admissions process. 

One said that “it was extremely difficult to decide whether to send test scores to colleges or not, because we don’t a poor score to hurt our kid”

Another agreed, questioning “how much time colleges actually spend going over each of the thousands of applicants every year.”

Just based on these two short quote alone, we already see some skepticism of the whole “test optional thing”. Now, let’s see if Game Theory can help 🙂


Let me break it down for you:

YEP, you read that right: based on the calculations above, the average college admissions officer at a top school spends just 3 minutes on your application. That means that in the time it takes to toast bread in a toaster, an admissions officer has summed up 16-17 years of your life. That’s crazy!

Something else to keep in mind:

Many of the assumptions made above are conservative values. For example some of the UC (university of California) schools got over 100,000 applications. Much of the Ivy League saw a 20% increase in applications with over 60,000-70,000. 


With these staggering facts in mind, let’s get to the fun stuff: Game Theory!


Game Theory Matrix Model


As seen in the model and matrix above, the best way for a student to maximize their chances at a specific university during a test optional cycle is through submitting a test score. 

To derive this solution I used the nash equilibrium model as well as the pareto optimal model. I also used optimization and movement diagrams to find the saddle point of the matrix, and thus, the solution to the game. To the non-game theorist mind, what does all this mean. Essentially, I took the different possible scenarios of applying with and without test scores as well as outcomes for the colleges, and mapped all that onto a 2×2 matrix. With a matrix made, we can now use various game theory techniques to break down what we have. For this specific project, I decided to go with both movement and pareto optimal diagrams. I analyzed all the different utilities and choose one that maximized the benefit to both players (applicant and college).


What can we takeaway from this:

Just based on the sheer amount of (or lack thereof) time that AOs spend on each application, submitting a good test score leaves no doubt whether an applicant is “smart enough” for a school. By not submitting a test score, AOs are left to spend valuable minutes deliberating whether you are academically prepared or not to attend that specific university. Through a lens of game theory we see that in order to set oneself up for the best shot at college admissions in years to come, one must submit test scores. 


Works Cited:


Let me know what you think! Leave a comment below


Leave a Reply