Game Theory, College Admissions, and the Early Decision Dilemma

1
Game Theory, College Admissions, and the Early
Decision Dilemma
2
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).

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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?

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The Game of College Admissions

• College Admissions . . .
• information/data
• - School What is the applicants
  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?

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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 consultpresidents, provosts, and deans of
  admissionsto 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.

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The Game of College Admissions

• Prestige/Selectivity
• SAT/ACT averages
• Admissions rate
• (what of applicant pool you offer admission
  to)
• Acceptance rate (doesnt 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-alternative
  s the applicant has thus, it shortens,
  simplifies and tilts the game of admission in
  favor of the university/college)

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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.

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College Admissions

• BUT
• 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 EDs
  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)

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College Admissions

• BUT
• 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 EDs
  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)

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College Admissions The Organization Kid

• 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.

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College Admissions The Organization Kid

• How 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 theyre 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 Dont 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 9th 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.
• --------------------------------------------
• Colleges/Universities newest addition to the
  game theory ritual of admissions
• - extensive wait-listing of qualified applicants
  (students response apply to 20 schools)

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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

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The Organization Kid

• Infancy
• - 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)

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The Organization Kid

• Elementary Schools
• - backpacks getting bigger, much bigger
• - April 26, 1983s 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)

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The Organization Kid

• Adolescence
• - 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

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The Organization Kid

• vs. 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 SATs 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 SATa
  test of specific bits of information set up in a
  format that tricks you into choosing wrong
  answersused 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.

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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.

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Prisoners Dilemma Games

• On 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

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

• Advertising Dilemma

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Prisoners Dilemma Games

• New 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 didnt 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 wouldnt 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.

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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 Cant 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 brink
• e.g., Contract Negotiations Labor Strikes
  (e.g., NHL, Reagan and the air traffic
  controllers strike in 1981)