Game Theory, College Admissions, and the

Early Decision Dilemma

What is Game Theory?

• It is the science of rational behavior in interactive situations.

• It takes the lessons learned from expected utility (EU) theory -- how we expect an individual to behave or to make decisions -- and then adds an interactive element (which is the interaction with another individual or institution that is also seeking to maximize their utility by acting rationally).

What is the key item in games?

INFORMATION / DATA!

Is information complete or incomplete?

Is information symmetric or asymmetric?

Are moves, based on this information, simultaneous or sequential?

The Game of College AdmissionsCollege Admissions . . .

information/data:

- School: What is the applicant’s intentions/desires?

- School: What will the applicant do if offered admission?

- School: How much will this student “help” the school?----------------------------------------------------------------------------

- Applicant: How much financial aid is the school willing to offer?

- Applicant: What do I need to have to be offered admission?

- Applicant: Would this be the “best” school for me?

How are Colleges/Universities Ranked?

Peer assessment (weighting: 25 percent). The U.S. News ranking formula gives greatest weight to the opinions of those in a position to judge a school's undergraduate academic excellence. The peer assessment survey allows the top academics we consult—presidents, provosts, and deans of admissions—to account for intangibles such as faculty dedication to teaching. Each individual is asked to rate peer schools' academic programs on a scale from 1 (marginal) to 5 (distinguished). Those who don't know enough about a school to evaluate it fairly are asked to mark "don't know." Synovate, an opinion-research firm based near Chicago, collected the data; of the 4,089 people who were sent questionnaires, 58 percent responded.

Retention (20 percent in national universities and liberal arts colleges and 25 percent in master's and comprehensive colleges). The higher the proportion of freshmen who return to campus the following year and eventually graduate, the better a school is apt to be at offering the classes and services students need to succeed. This measure has two components: six-year graduation rate (80 percent of the retention score) and freshman retention rate (20 percent). The graduation rate indicates the average proportion of a graduating class who earn a degree in six years or less; we consider freshman classes that started from 1996 through 1999. Freshman retention indicates the average proportion of freshmen entering from 2001 through 2004 who returned the following fall.

Faculty resources (20 percent). Research shows that the more satisfied students are about their contact with professors, the more they will learn and the more likely it is they will graduate. We use six factors from the 2005-06 academic year to assess a school's commitment to instruction. Class size has two components: the proportion of classes with fewer than 20 students (30 percent of the faculty resources score) and the proportion with 50 or more students (10 percent of the score).

In our model, a school benefits more for having a large proportion of classes with fewer than 20 students and a small proportion of large classes. Faculty salary (35 percent) is the average faculty pay, plus benefits, during the 2004-05 and 2005-06 academic years, adjusted for regional differences in the cost of living (using indexes from the consulting firm Runzheimer International). We also weigh the proportion of professors with the highest degree in their fields (15 percent), the student-faculty ratio (5 percent), and the proportion of faculty who are full time (5 percent).

Student selectivity (15 percent). A school's academic atmosphere is determined in part by the abilities and ambitions of the student body. We therefore factor in test scores of enrollees on the SAT or ACT tests (50 percent of the selectivity score); the proportion of enrolled freshmen (for all national universities and liberal arts colleges) who graduated in the top 10 percent of their high school classes and (for institutions in the universities-master's and comprehensive colleges-bachelor's categories) the top 25 percent (40 percent); and the acceptance rate, or the ratio of students admitted to applicants (10 percent).

Financial resources (10 percent). Generous per-student spending indicates that a college can offer a wide variety of programs and services. U.S. News measures the average spending per student on instruction, research, student services, and related educational expenditures.

Graduation rate performance (5 percent; only in national universities and liberal arts colleges). This indicator of "added value" shows the effect of the college's programs and policies on the graduation rate of students after controlling for spending and student aptitude. We measure the difference between a school's six-year graduation rate for the class that entered in 1999 and the rate we predicted for the class. If the actual graduation rate is higher than the predicted rate, the college is enhancing achievement.

Alumni giving rate (5 percent). The average percentage of alumni who gave to their school during 2003-04 and 2004-05 is an indirect measure of student satisfaction. To arrive at a school's rank, we first calculated the weighted sum of its scores. The final scores were rescaled: The top school in each category was assigned a value of 100, and the other schools' weighted scores were calculated as a proportion of that top score. Final scores for each ranked school were rounded to the nearest whole number and ranked in descending order. Schools that receive the same rank are listed in alphabetical order. Our rankings of accredited undergraduate business programs and engineering programs are based exclusively on peer assessment data gathered from the programs' deans and senior faculty members.

The Game of College AdmissionsPrestige/Selectivity:

SAT/ACT averages– Admissions rate

(what % of applicant pool you offer admission to)– Acceptance rate (doesn’t change much)

Yield rate: percentage of accepted applicants who enroll= (offers accepted offers of admission)

So . . . Early-Decision helps increase information on both sides (while also limiting the number of sequential steps-options-alternatives the applicant has = thus, it shortens, simplifies and tilts the “game” of admission in favor of the university/college)

College Admissions• university needs 2,000 students in its incoming

freshmen class

• It receives roughly 12,000 applications

• If yield rate has traditionally been around 33%, it means university needs to make about 6,000 offers of admission (or acceptance letters), which means the university will have a 50% acceptance (or selectivity) rate.

College AdmissionsBUT…

• Early-Decision (25% of freshmen class or 500 students)

• Acceptance Letters: 500 to ED applicants (to bring in 500 ED students) and 4,500 acceptance letters to regular applicants (to bring in 1,500 regular students)

• TOTAL = 5,000 Letters/Offers (all the ED’s enrolled because of “binding” condition) – originally 6,000 Letters/Offers

• So, selectivity improves to 42% (from previous 50%) and the yield rate improves to 40% (from previous 33%)

College AdmissionsBUT…

• Early-Decision (50% of freshmen class or 1,000 students)

• Acceptance Letters: 1,000 to ED applicants (to bring in 1,000 ED students) and 3,000 to regular applicants (to bring in 1,000 regular students)

• TOTAL = 4,000 Letters/Offers (all the ED’s enrolled because of “binding” condition) – originally 6,000 Letters/Offers

• So, selectivity improves to 33% (from original 50%) and the yield rate improves to 50% (from original 33%)

The “Power of Context” (Stanford Prison Experiment, N.Y. Subway system, etc.) -- Michael Thompson: “College has achieved a symbolic importance so out of proportion to its actual meaning, and the admission process has evolved into such a Byzantine ritual, that it can make normal people act nutty and nutty people act quite crazy.”

Thompson: “The frantic involvement of many parents in the application process is often a cover for this profound parental anxiety:

Did I do a good job with this child? Did I do everything I needed to do for this child? Is this child prepared? Is this child going to have a good life? Etc.

College Admissions & The Organization Kid

College Admissions & The Organization KidHow do you get accepted in this game theory world of college admissions?

(Wall Street Journal)

(1.) Play the Oboe, and play it well. The old ideal of the football player-Latin scholar-thespian is passé. Many schools now prefer to see a lot of talent in a specific field, though exactly what they’re looking for varies. Colleges are looking more for a well-rounded class and less a well-rounded kid.

(2.) A Summer with Us. A growing number of schools, like Brandeis and Harvard, are trying to get to know potential applicants by offering summer programs. Some let high-school kids take college courses and earn college credit.

(3.) Move to Idaho: Don’t laugh. Colleges/universities do want geographic diversity.

(4.) Get a Life. Consider taking a year off after high school. A survey by the National Association for College Admission Counseling found that extracurriculars ranked 9 th in importance, behind grades in college-prep courses (1st), teacher recommendations (6th) and even the interview (8th). Take time to develop into a more complete human being.

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Colleges/Universities’ newest addition to the “game theory” ritual of admissions:- extensive wait-listing of qualified applicants (students’ response: apply to 20 schools)

The Organization Kid• Future Workaholics of America (FWA)

• the “meritocratic elite”

• 1981-97: Time-Analysis Studies at the University of Michigan

- amount of time children 3-12 spent playing indoors declined by 16%

- time spent watching TV declined by 23%

- amount of time spent studying increased 20%

- and the amount of time spend doing organized sports increased by 27%

The Organization KidInfancy:- children are shaped by the interaction of their DNA and

their environment, hence …

- good parenting starts pre-birth:

“neurological stimulation”

Mozart for Babies, etc.

- helps to build a strong web of brain connections (synapses)

The Organization KidElementary Schools:

- backpacks getting bigger, much bigger

- April 26, 1983’s “A Nation at Risk”

published by the Dept. of Education

- new emphasis: testing, accountability, and order

- the Christmas toy of 2004: the Time Tracker

(recommended ages: 4 and up)

The Organization KidAdolescence:

- 1997 “National Longitudinal Study of Adolescent Health”: emphasized that the most powerful factor in determining the well-being of young people is the presence of parents and adults who are actively engaged in supervising and setting goals for teenagers’ lives

- parental authority rests on 3 pillars:

science, safety, and achievement

The Organization Kidvs. Judith Rich Harris and “peers”

- Based on empirical research, how different do parents appear in these two rival theories of adolescent/young adult behavior?

Years of Hard Work, then a Low SAT Score (View from a High School Senior):

“My SAT scores arrived in the mail today. By college entrance standards, they were low. I am a senior. I love school, but I cannot perform on standardized tests. The pressure of having to produce answers without time to reflect incapacitates me.

I have been waiting for these scores because, more than any other factor, they will tell me to which colleges I have access. When I opened the envelope from the Admissions Testing Program and looked at the scores, I felt as if a knife were driven through my heart. I an in the top 8 percent of my graduating class of 500 and am in the National Honor Society. But these things are not enough. I am also expected to achieve a certain score on the SAT’s to gain entrance to the colleges I have chosen.

I have to think about thing before I can act. But on the SAT you have to act fast. Why is it better to be able to answer a question quickly than to take time with it? And why is the SAT—a test of specific bits of information set up in a format that tricks you into choosing wrong answers—used as the ultimate national standard?

Where is the test that measures the effort that I have put in and the progress I have made in high school, that shows how well I can reason and think about issues, that shows how much I want to contribute to society?

I am sitting on my bed thinking that the years of effort made in school have been diminished, or even erased, by this one test. I am crushed that as of today my options are narrowed because I have been viewed through one lens that has the power to shape my future but through which I cannot be seen in my entirety.”

Game Theory & “Prisoners’ Dilemma”The most studied game in business is the prisoners' dilemma. It illustrates a fundamental

tension between conflict and cooperation. Both prisoners would like to cooperate to minimize their sentences (lower right corner below), but face a large temptation to turn the other in. Consequently it is difficult to maintain such a cooperative agreement.

In the jargon of game theory, we say that such an outcome is not an equilibrium of the game. Equilibrium is reached in the upper left-hand corner: each competitor is doing the best he/she can given what his/her opponent is doing. Neither competitor can unilaterally make him/herself better off. Note that this is not an efficient outcome.

“Prisoners’ Dilemma” GamesOn a superficial level, the prisoners' dilemma appears to run counter to Adam Smith's idea of the

invisible hand. When each person in the game pursues his private interest, he does not promote the collective interest of the group.

Pricing Dilemma

“Prisoners’ Dilemma” GamesDiscussion Question: How did the tobacco companies’ profits change following the government's ban of over-the-air cigarette advertising?

Advertising Dilemma

“Prisoners’ Dilemma” GamesNew Jersey janitors and the SEIU (Service Employees International Union)

• 10,000 janitors who cleaned the office buildings in the cities and suburbs of northern New Jersey 7 years ago: only a fraction were unionized and they were making $10 per hour less than their counterparts just across the river in Manhattan

• Interestingly, employers didn’t like the low wages and poor benefits any more than the SEIU did; cleaning companies complained that they had trouble retaining workers and the workers they did keep were less productive

PROBLEM: for any one company to offer higher wages would have been tantamount to an army unilaterally disarming in the middle of a war; cheaper competitors would have immediately overrun its business

TRADITIONAL STRATEGY: for the union to pick the most vulnerable employer in the market, pressure it to accept a union and then try to expand from there

ALTERNATIVE: Organize the entire market at once, which the SEIU did by promising employers that the union contract wouldn’t kick in unless more than half of them signed it.

RESULT: The SEIU ended up representing close to 70% of the janitors in the area, doubling their pay from minimum wage to more than $11 an hour.

Strategic Moves & Brinkmanship Games• Strategic moves. A player can use threats and promises to alter other players' expectations of

his/her future actions, and thereby induce them to take actions favorable to him or deter them from making moves that harm him. To succeed, the threats and promises must be credible. This is problematic because when the time comes, it is generally costly to carry out a threat or make good on a promise. Game theory studies several ways to enhance credibility. The general principle is that it can be in a player's interest to reduce his/her own freedom of future action. By so doing, he/she removes his/her own temptation to renege on a promise or to forgive others' transgressions. - For example, Cortés burned his own ships upon his arrival in Mexico. He purposefully eliminated retreat as an option. Without ships to sail home, Cortés would either succeed in his conquest or perish. Although his soldiers were vastly outnumbered, this threat to fight to the death demoralized the opposition; it chose to retreat rather than fight such a determined opponent.

• Brinkmanship. Consists of deliberately creating a risk that if other players fail to act as one would like them to, the outcome will be bad for everyone. Introduced by Thomas Schelling in The Strategy of Conflict, brinkmanship "is the tactic of deliberately letting the situation get somewhat out of hand, because being out of hand may be intolerable to the other party and force his/her accommodation."

- For example, when mass demonstrators confronted totalitarian governments in Eastern Europe and China, both sides were engaging in just such a strategy. Sometimes one side backs down and concedes defeat; other times, tragedy results when they fall over the brink together.

e.g., “We Can’t Take the Exam Because We Had a Flat Tire.”e.g., Why are professors so mean about final exams and extensions?e.g., roommates and families on the brinke.g., Contract Negotiations & Labor Strikes (e.g., NHL, Reagan and the air traffic controllers’ strike in 1981)