# Game Theory—Final

As my math independent research draws to a close, I start to ponder how I can tailor the information I learned through my research to a large audience with no math or economics background. Even though I have learned a variety of methods of payoff calculation, I want to use the most basic model to explain what I have learned, especially on how game theory can differ from the reality.

A month ago, I did a mini-research on Westtown Dining Hall’s seating arrangement. The attached picture is an expected payoff model.

This graph can be interpreted as depicting the highest theoretical payoff is reached when a balanced amount of people from different ethnicities sitting at a table. However, if a table is filled with people from the same ethnicity, the payoff will only be half of the payoff when the table has people from different cultural backgrounds. This is because people can benefit more from cross-culture talks and making new friends. What I am confused about is how the theoretical payoff differs from the reality. Do people want to have cross-culture talk and to make new friends? Therefore, I wrote a survey recently and hope to find out how different reality is from theory.

The form below is a small survey that I am going to hand out:

Independent Research on Westtown Dining Hall Policy

1. Which one would you prefer?

Choosing your own seat                      Being randomly assigned to a seat

1. If you are randomly placed to a table, please select your anticipated degree of comfort with your situation:

(0-dislike 0.5-indifferent 1-prefer)

0          0.25     0.5       0.75     1

1. If you are allowed to sit at a table of your choice, please select your anticipated degree of comfort with your situation:

(0-dislike 0.5-indifferent 1-prefer)

0          0.25     0.5       0.75     1

Joe

The survey above will allow me to draw a graph and to compare reality with theory. Even though the result might not be accurate because of the limited sample size, it will be interesting to see how large the deviation is from the theoretical graph.

As T.Elson suggested, I will then be able to analyze whether we should randomize students or allow students to sit with people with whom they like to sit. Ideally, students have to be objective and should not choose an answer based on their preferences but on their judgments of the situation. During the research, I will try my best to force my sample to be but there is no way that I can control their objectivity. Therefore, by conducting a research, I will probably be able to figure out students’ preference on this topic. One thing I can draw from students’ responses is whether students prefer to stay in their comfort zones or to reach out.

Despite all the math and graphs, it remains an interesting topic to discuss. Do we want to force students to gain more benefit from their experiences? Or should we just let students make their own decisions and stay within their comfort zones. Should we always maximize the payoff of students’ experiences or should we give them some personal room for freedom and choices? Do personal freedom included in the payoff of students’ experiences? In the end, we should probably reconsider the definition of payoff: what is included and what is not.

Here are some Game Theory Websites and articles that I have been reading, and they all shed lights on my topics: Economist.com, How to Make a Game, Game Theory and the Real World.

Work Cited