Warrior Words: Playing with game theory
As much as we seniors would like to breeze through the final month of classes deemed the fourth quarter and sail into our enjoyable, interesting internships and on to summer bucket lists, there is one single undeniable albatross that stands between many seniors and the sunny, test-free future: AP exams. AP exams are the first two weeks of May, and the scores of the rare 1, disappointing 2, almost-there 3, acceptable 4, or esteemed 5 are released over the summer. No one really understands AP exams’ purpose or importance, aside from hopefully testing out of some prerequisites in college, yet the majority of students who take an Advanced Placement course opt to take the exam. It’s three hours of saturated, dizzying, specific multiple choice and free response questions that demand a dive into the depths of a year-long course and hours of pre-test cramming.
They say you only really know something when you can teach it to someone else, so I’ll be studying for my AP Microeconomics test by analyzing game theory in terms of a crowd at a Wilton High School football game.
Game theory is an essential concept in economics, computer science, and poker that explores conflict and cooperation during interconnected decisions. There are players, rules, consequences, and payoffs. Nash equilibrium is the solution concept at which both players pick their best option. Game theory does have many real-life applications and is apparently getting pretty trendy.
If you’ve never stood in the students’ section of a WHS football (or lacrosse!) game, I’ll let you know: it’s awesome. There are leaders, chants, themes, great tunes and fun people. Just one key detail: everyone stands.
It is tradition, but wouldn’t it just be easier and more comfortable if everyone sat? What does our trusty mathematical model have to say about it? Let’s look at it this way: there are two WHS fans, obviously decked out in blue and white gear and exuding WHS pride. If one sits and the other stands then the sitter gets a 5/10 view (he’d be obstructed by standers) and the stander gets a 10/10 view. If both stand then each will have a 7/10 view. If both sit then each will have a 9/10 view. In this model, both will stand even though sitting would produce the greatest happiness for society. Why is that? Let’s say Fan B sits. Then Fan A would choose to stand and get the 10/10 view. Let’s say Fan B stands, then Fan A would have to stand to get the 7/10 experience over his 5/10 option. In order to achieve the best option, all students would have to agree to sit, an unlikely prospect considering the tradition of intense, standing fans and the dominating seniors who demand such. This roaring crowd of standing students is the Nash equilibrium.
So, did I earn a 5?
Olivia Phelan is a senior at Wilton High School. She shares this column with four classmates.