Today, I’m going to examine with you, in the lens of Game Theory, some of the most memorable times at Westtown, Community Weekend Events!
As we all know, as a boarder at Westtown, we are required to attend four community weekend events each year. In these events, we have the common goal to have a great time and build a tighter community. But, what makes these events fun?
People, of course! For example, let’s say that there’s going to be a classical “Capture the Flag“, we would want a lot of people to join the game (the more the merrier).
When the announcement of the “Capture the Flag” weekend event is made in collection, everyone faces the same decision of whether to join the game. If I join the game and over half of the school is there, we will have a great time together. Yet, if I join but only a few people (less than 20 people) are there, I will feel I’m wasting our time and am better off watching Netflix in bed. On the hand, if I do not join, I won’t gain anything from event.
In this situation, it is not plausible to draw out the pay off matrix for all players (there’s over 300 of us after all). Yet, I could consider my best response in each situation. If there’s a lot of people, I would be better off going to the game. If no one’s there, I should not go.
Evidently, there will be a lot of discussions about “Capture the Flag” as we all try to gather others’ responses to inform our choices. By the end of the week when we put everyone’s best response together, we are likely encounter a new concept in Game theory called Nash Equilibrium.
A Nash Equilibrium is a situation in which all players are playing their best responses to others strategies, and thus do not have an incentive to change their decisions. For example, in this situation, there are only two Nash Equilibria: everyone in or everyone out. For if everyone is in the game, we will have a fun time and no one would regret their choice of coming. On the other hand, if everyone is doing something else, there would be no game at all and nothing to regret about. Any situation in between, some people would either regret going (if there’s not enough people to have a good time), or not going (missing out on a fun memory).
Yet, the question arises, which equilibrium will we reach at the end of the week? The good equilibrium where everyone have a great time, or the bad one where nothing happens?
Well, the answer is, the result is not up to our Game Theory model, but up to our personal expectations. If everyone has faith that we will have a good time, then we will. Otherwise, we won’t.
At these times, what the community truly needs is a leader who can help sway the public expectation to the positive side so everyone will go and have fun!
Here, the importance of student leadership as well as collection and weekend board publicity are demonstrated by Game Theory!