Public State College Acceptance and Wealth: Game Theory
It is no question that public state colleges accept more in-state students than out of state students. Most public colleges are funded by the state and therefore in-state students have an advantage over out-of-state students. In-state students receive cheaper tuition and have higher acceptance rates than out-of-state students. Despite the cost difference, according to the article linked below, higher tuition in out-of-state public schools is not stopping a certain pool of students from applying. Students who come from wealthier families are increasingly applying to more colleges, many of which are these out-of-state public schools because they have the means to do so. Many public colleges such as the University of Wisconsin-Madison have picked up on this trend and are taking advantage of the new flux of out-of-state applicants. The percentage of out-of-state students have increased in many public colleges and universities which is beneficial to the colleges because they earn greater profit per class of students.
This situation can be analyzed using game theory. The public colleges’ decisions with regards to whether they accept or reject the wealthy out-of-state students and whether these students (if accepted) accept or deny their admission affect the payoffs of both parties. Take a look at the diagram below:
The payoff for both the student and the college varies depending on whether the student accepts or denies admission. If we give values to the expected payoff for each decision, we may expect a result like this:
Of course, public colleges benefit monetarily from accepting students out-of-state. If those students accept the admission, the students themselves will also benefit (though not as much as the college does) by having a seat in the incoming class. They may have avoided other colleges that are even more expensive. Since we are also exclusively talking about wealthy out-of-state students, these students most likely do not have a problem with paying the higher tuition (though this is just an assumption for the sake of the example diagram above and does not necessarily reflect each individual’s circumstances). If the wealthy out-of-state students decline admission however, both parties still benefit (though not as much as the first result) because now the college has more room to accept other students (who may or may not be in-state) and the students who declined have the opportunity to explore other options, some of which may be less costly. However, if the student is rejected when they would have accepted the admission, they lose security because they might not have other colleges to fall back on. Their only benefit would be the possibility of being accepted into another college that has a lower tuition. The college would benefit from rejecting this student (not to the same degree as if they had accepted the student) because they can accept other students.
The scenarios depicted using game theory show that any situation in life especially when two different parties are involved is a game where the actions of one affect another. Based on the potential outcomes of the diagram above, the dominant strategy is A-B.
Link: https://secure.marketwatch.com/story/why-big-public-colleges-are-increasingly-dominated-by-wealthy-students-2016-04-08