# 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

# Game Theory—Uncertainty

Uncertainty continues to play a big role in Game theory. In trying to make good choices, people have to use their own judgment and discretion rather than math equations, because math equations cannot accurately represent uncertainties within a situation.

# Game Theory—Sequential Game

Most of the games I have described so far could be categorized as games that are played simultaneously. Regardless of whether it is rock-paper-scissors game or the prisoner’s dilemma, each player can anticipate his/her opponent’s response to some extent, but does not know his/her strategy for sure. Even though the notion of Nash equilibrium provides a reasonable way for people to surmise each other’s strategy under the assumption that everyone is rational, each player still cannot conclusively determine what strategies his/her opponent will play until his/her opponent has played it. Now, the course shifts its focus into sequential games, where a player can make a decision based on the strategy that his/her opponent has played already.

# Game theory—More Thoughts on Segregation Model

After talking with my mentor T. Elson last week, I was inspired by his comments because they shed new light on my independent project. We primarily talked about the segregation model where the method of randomization can help achieve Nash equilibrium and thus providing a fair result in some situations. However, there is a distinction between an optimal situation and Nash equilibrium. Nash equilibrium only indicates that people are playing the best response corresponding to their opponents’ strategy, while an optimal situation indicates that each person receives the highest possible payoffs. A game with three Nash equilibria might only have one optimal situation.

# Economics and My Life

Economics has always been a topic that intrigued me, probably because both of my parents are currently in this field. Even though I understand that my parents’ career should not influence my own career decision, I have learned to appreciate their efforts as well as the influence of economics has had on our family. When my parents graduated from college, their families could barely support them. With fifty dollars (which is equivalent to three hundred yuan) in their pockets, they went to seek career opportunities in a southern city of China—Shenzhen, once a small fishing village but now a major city in China with a vibrant economy. They eventually made a living by their endeavors and the fortuitous decision to go to Shenzhen. In the 90’s, Shenzhen became a special economic zone in China and developed rapidly with the “reforming and opening” policy, which led to a significant increase in foreign investments. With this opportunity, my mother created her own startup company and my father joined a state-owned enterprise. The prosperous economy in China gave them hope to achieve a higher standard of living.

# Game theory and its limitations

Last week, I explored the idea of randomization in my former blog from a mathematical perspective. As the professor claims in the lecture, he believes that randomization is a great way for solving complex social problems, because it can always achieve fair results. However, there are limitations. These limitations intrigue me, for they remind me that math is not a perfect tool that can solve every real world problem. Therefore, in the process of doing math, not only do I need to search for a correct answer, but I also need to be aware of the fact that the eventual outcomes and inferences may not always provide perfect solutions in reality. While using multiple mathematical equations and models to generate a grand theory present us with a logical way of thinking, the extrapolated theory has limitations under the light of reality. Such is the case of Game theory—it is well established but is also somewhat idealized.

# Game Theory—Segregation

In the lecture, the professor elaborated on the notion of the Nash equilibrium and introduced us to a novel idea called randomization. All the games I have shown in my previous blogs were categorized as pure strategy games, which means people always play the same strategy every time when there is a Nash equilibrium. For example, if you realize obeying school rules is a Nash equilibrium, you will keep following the rules every time because you are better off when you do so. Continue reading

# Game Theory—Dating Strategy

In the course, the professor introduced a game called “Battle of the Sexes” in order to further elaborate the notion and the application of the Nash equilibrium. He stressed that coordination is extremely important in our daily lives because different people have different interests. Therefore, I am going to be nerdy and to explain a situation during a date in terms of a Nash equilibrium so that we can draw meaningful lessons from it. Continue reading

# Game Theory—Third Week

This week, I continued making progress. The professor introduced mathematical language into the course, which slightly confused me. I am used to crunching numbers in my calculus class; however, using mathematical language to describe an abstract definition seemed unintuitive to me. Later on, I overcame this problem by simply copying down the definition while actively reflecting upon it. This way allowed me to grasp the mathematical idea behind the definition and get used to writing definitions in a mathematical way. Continue reading