I Want to Play a Game: A Game Theory Exercise on Early Decision

At Goldey-Beacom College, I teach several economics courses that cover the basics of game theory. Game theory is a branch of applied mathematics that provides tools for analyzing situations in which players make interdependent decisions. In my microeconomics course, I introduce game theory later, during the applications phase. It’s a useful tool when analyzing a competitor’s decision in the lens of rationality.

Most high school students applying to college are unaware of the game theory involved in the financial aid offer process. Over the next few months, I will introduce the concept of game theory into the college decision-making process to educate readers about the rationale behind their choices. It turns out that a student’s decision-making process for choosing a college to enroll in after high school involves a combination of economics, finance, marketing, and psychology. These disciplines weigh heavily on a student’s emotions, which is what institutions prefer when shaping a class.

Learning about the game theory aspects of the financial aid offer process in higher education will make you a better consumer of information that colleges and universities are selling to you daily.

Our first game theory scenario in this month’s newsletter is Early Decision. Early Decision is a college-admissions process that legally binds a student’s intent to enroll at a specific institution if they commit to that admissions track. Essentially, schools that offer this option argue to students the following premise: if you apply during our “early window,” you will have a better chance of admission than during the regular decision admit cycle. However, you must commit to us if you decide to submit an Early Decision application to our institution.

For those unfamiliar with Early Decisions, students can select only one college or university each year. Students who manipulate the system by selecting multiple colleges or universities in Early Decisions are subject to harsh penalties from participating institutions. Early Decision schools use a clearinghouse database to report their Early Decision admits, thereby deterring other schools from poaching their students.

So, without further ado, let’s introduce the players involved in this “game.”

Meet the Players

Early Decision is a simple payoff matrix between two players: the student and the institution of higher education. While other parties (e.g., parents) may influence a student’s decision to commit to a strategy, there are essentially only two players in the game, which makes our decision tree analysis much easier.

From the outset, students who engage in the admissions process known as Early Decision benefit from improved odds of acceptance compared to the regular decision admit cycle. Students also face a significant drawback: the inability to compare or accept financial aid offers from other schools. Once their Early Decision school admits them, all other alternatives cease to exist.

(In actuality, students can break an Early Decision commitment since Early Decision is not a legally binding contract under U.S. contract law. That said, it does tarnish a student’s image and credibility with other schools that participate in the Early Decision admissions game, which can prompt them to rescind current offers or restrict future admissions decisions. Schools view students who do not follow through with their Early Decision admission decision as academically dishonorable. There are only a few cases where a school may accept a reason as valid for breaking an Early Decision commitment.)

Reservation Price

Game theory also involves the concept of the reservation price. Reservation price is the minimum price a seller is willing to accept or the maximum price a buyer is willing to pay. Throughout a game-theoretic exercise, buyers and sellers reveal their preferences to each other about their ability to buy or sell at the prevailing price levels.

The reserve price in this theoretical game of Early Decision is the school’s full cost of attendance. So, when a student applies to a school through an Early Decision program, they are essentially revealing the following. At a minimum, I consider this school’s full cost of attendance affordable and enticing. Whether or not a student can afford that school’s cost of attendance is a different story.

Imagine a student who applies to University A through its Early Decision program. The school’s current cost of attendance is $50,000 per year before any financial aid. When a student submits an Early Decision application to this school, they are essentially revealing the following information to the enrollment management team: I enjoy your school so much that I am willing to pay the full cost of attendance while giving up all other alternatives.

Game #1: Early Decision

Figure 1: An Early Decision simulation of the financial aid offerings available to students who participate in this game.

Explaining the Results of Our First Game

In our first payoff matrix, we have two distinct scenarios for when a student applies to a school through their Early Decision application process. Let’s first start with the worst outcome imaginable: denied. A denied entry means there’s nothing else they can do at that school for the current admissions cycle. Basically, the game is over for the student at that stage. While students are free to pursue other schools in the Regular Decision cycle (or another school’s Early Decision admissions process if their window is still open), their odds of attending this school are effectively null and void.

Now, in the event a student receives admittance to their Early Decision school, a new game commences: the financial aid offer.

Every school supplies a student with a financial aid offer that details their anticipated direct and indirect costs, and their overall financial aid package. Schools usually depict a student’s net cost before self-help aid to help students understand the full scope of loan usage at that school. Now, in a Regular Decisions admissions process, schools are hyper-competitive in their pursuit of students. Are those schools more likely to dangle attractive financial aid packages than Early Decision schools?

It depends. Revising our discussion on the reserve price. When a student submits an Early Decision admissions application to a school, they signal their intent to attend the school at all costs, including the school’s full cost of attendance. What incentive does a school have to produce a generous financial aid package at this stage? Most likely, there is not much incentive to do so.

Students are stuck in a difficult predicament at the phase if their financial reality does not match a school’s published cost of attendance. Schools have two options at this phase: offer a generous financial aid package that combines merit and need-based aid, or stick a student with little to no scholarship assistance. While it is possible for a school to award a generous financial aid package to an Early Decision admit, it’s equally true that the odds of it happening are not plentiful. In this stage of the game, the institution has the dominant hand: they know you have little to no other options and from the start you revealed to the institution that you intended to attend at any cost.

Information Asymmetry

In a normal admissions cycle, sans all the fancy Early Admit or Early Decisions application methods, schools and students know very little about each other. This dilemma leads us to our next concept in game theory: information asymmetry. Information asymmetry is a situation in which one party possesses superior knowledge to another in a transaction or decision-making process, thereby affecting outcomes, pricing, market efficiency, and the overall strategy of each participant.

A classic example of information asymmetry is the used car market. Buyers of a used car know little about its quality or past. Sellers tend to know the most about vehicles. Although tools are available to mitigate the unknowns in this example, such as the vehicle’s accident history on CARFAX, each side is naturally suspicious of the other. The buyer has an incentive to avoid purchasing a “lemon.” The seller has an incentive to sell their vehicle at the highest price possible, even if it is not entirely realistic given the car’s history or issues. Transactions in this market are not entirely efficient as the final sales price may not reap what each side wanted.

In higher education, enrollment management teams are acutely aware of information asymmetry battle between prospective students and their institutions. In a Regular Decision admissions cycle, colleges have limited information on a student’s enrollment intent. Sure, there are fancy tools to gauge an admitted student’s interest in the school, but for the most part, their decision to enroll does not happen until the last possible moment (decision day). Institutions generally do not know where their school lands on a student’s radar. Are we their top choice? Safety school? Aggressive play if all the signs align on the same night?

Institutions prefer students to signal (reveal) their intent sooner rather than later. Expending too much money on a financial aid offer early in the process for a student who was already going to attend is not a productive use of money (although it sure does make a student very happy to receive a generous financial aid package!). In an ideal world, schools aim to award financial aid as equitably as possible. Students with the means to pay tend to pay more out of pocket than those with limited means.

Early Decision is a classic signaling game in our game theory exercise. By creating a binding decision in the application process, schools get applicants to signal their “top choice” earlier, thus avoiding the negotiation process. An Early Decision acceptance also forgoes all your alternative options in the negotiation process for additional financial aid.

Both Sides Face Risk—Humans Detest Risk

The following statement should not come to a shock to anyone in this world of ours: humans detest risk. Our ancestors did not do well with risk either. It’s a trait we inherit from our DNA.

Probability evaluation is a set of tools that we use daily to determine our next action or choice. Daniel Kahneman, a renowned psychologist and researcher, famously wrote in his book Thinking, Fast and Slow that we have two systems in our brains to determine our next course of action. Our first mental system thinks quickly and decisively. Our second mental system is more reflective and analytical.

A survival mechanism that humans generally struggle with is probability evaluation. When confronting unknown odds, we tend to overestimate what will happen. In a normal college admissions cycle, applicants generally have a 50-50 chance of receiving an admittance decision (assuming, of course, they meet admissions standards). Applicants dislike that uncertainty even though the 50-50 odds are generally considered a fair bet.

Applicants exhibit risk aversion. Risk aversion is the tendency of individuals or economic agents to prefer certainty over uncertainty, prioritizing the avoidance of potential losses even if it means accepting lower expected returns. When a student applies to a school through their Early Decision application process, they are trying to improve their odds of a positive outcome. This concept leads to an intriguing research question: does a student experience more pleasure or pain with an Early Decision acceptance or denial? In terms of risk aversion, students are probably feeling more dejected with denial and more happiness with acceptance.

If you talk to the average person about risky gambling, most will prefer a certain outcome over an uncertain one. That reason alone is why insurance is one of the most sought-after financial products. The stakes are high in the admissions game. Improving one’s odds through Early Decision may seem like the right thing to do to prevent the pains of loss aversion. Loss aversion is a cognitive bias where the pain of losing is psychologically stronger than the pleasure of gaining an equivalent amount. When a student opts out of Early Decision and applies through Regular Decision, they are taking a significant gamble: reduced odds of acceptance. But is that a rational way to think or believe?

Since students’ dislike uncertainty, Early Decision gives them an edge, even if it is a perceptive edge, to improve their acceptance odds. While a rejection in the Early Decision phase is painful, it may not be as painful than during the Regular Decision phase, where doubts creep in with thoughts of, “if I had just improved my odds by applying through Early Decision…”

These cognitive shortcuts (heuristics) relieve our brains from the paralysis of analysis. It can also lead to excessive optimism about an outcome. This heuristic is known as optimism bias. When a student applies through Early Decision, they perceive their application has an edge over a person in the Regular Decision pool. This optimistic view is not correct. While the odds of acceptance improve when applying through Early Decision, an applicant may underestimate the risk of a negative outcome (rejection). This optimism bias can cloud a student’s judgment about the best course of action in the game of Early Decision.

Institutions also face risk—and it’s the exact reason why they hold the dominant hand in the Early Decision game. A college or university’s objective is to maximize net revenue potential while shaping the cohort’s academic profile in a manner that satisfies the institution’s yield rate goals. In a nutshell, colleges and universities try to offer the minimum amount of financial aid (merit- and need-based) required to persuade students to attend their school rather than a competitor. Enrollment objectives differ at most schools. At the end of the day, though, it all comes down to the total number of students enrolled. What better way for an institute to reduce its risk than by shaping its class early and often through Early Decision?

Applicants have a different objective from institutions. Their objective is to maximize the perceived educational value while minimizing costs. Both parties have differing priorities, which typically makes this game more strenuous in a fair and competitive marketplace (i.e., no Early Decision). A student’s goal during the negotiation process with schools is to create an aura of credible threat that at any point in time they can walk away from College A while defecting to College B. In this scenario, schools must compete amongst each other to meet their enrollment aims. Discounting (a.k.a. additional scholarships) becomes more prevalent. Students inherit consumer surplus at this stage while institutions see a reduction in their producer surplus.

One More Game to Chew On: A More Complex Early Decision Game Exerise

Figure 2: A simulation of an Early Decision exercise where a student decides between three choices: Reach School, Safety School, and Regular Decision Schools.

In a 2007 paper, researchers Ayse Mumcu and Ismail Saglam noted that when students settle for “safety school” during the Early Decision process, colleges gain leverage over other competitors because it removes those high-quality students from the admissions pool as a potential enrollee.

Figure 3: Prisoner’s Dilemma Aspect to this Game

What Does This Mean for Students and Their Financial Aid Offer?

Early Decision signals to a college that the applicant has a serious intent to enroll there at the current reserve price (i.e., the institution’s full cost of attendance). By signaling too early, students forego their alternative options and lose leverage in financial aid negotiations. Only students who can confidently pay the full reserve price should opt for this strategy.

Students who need competitive financial aid offers to afford their postsecondary education should eschew Early Decision when possible. Although the odds in the Regular Decision process are relatively equal (50-50) compared to Early Decision, which features significantly better chances, your ability to negotiate a competitive financial aid package is much better in this scenario. Price-conscious students are better off applying through Regular Decision than Early Decision. A caveat to this thinking would be that an Early Decision school might have a generous financial aid program for students with exceptional financial need.