A Workshop on Game Theory Introduces Us to Mathematical Modeling
With just a few days of the school year under our belts, we had a guest stop by Long-View and take us through a workshop on a very high level topic: Game Theory.
Dr. James Spindler is a professor at UT in both the business school and law school and holds both a JD and a PhD in Economics. He came to teach us about economics and more specifically, game theory, which is the study of mathematical models of conflict and cooperation and is used in economics, as well as other disciplines.
Dr. Spindler started us out thinking about some traditional economics questions, such as: How do we allocate resources? How do we get the resources to go where they are supposed to go? After a brief discussion, we moved onto to our first problem to consider, which effectively introduced us to The 1st Welfare Theorem. A rancher has steaks, a farmer has potatoes, but each would be better off with some of the steaks and some of the potatoes. What is required to make them best off?
After delving into this situation, we then moved to talking about Gary Becker, who is an economist who writes on crime and punishment. This led us to discuss why people commit crime (Marin offered up the idea that people may do so for revenge while Euan mentioned that people sometimes steal for good or “benevolent” reasons). This brought us to learning about The Prisoner’s Dilemma.
The Prisoner’s Dilemma is a classic scenario in which two people are both going to jail, but are offered the opportunity to accuse the other, alongside a system of rewards and punishments. The idea is to predict what choice each will make after looking at the situation through a mathematical model. The kids broke into groups to attempt to do this with 2 x 2 matrices in order to better understand the best strategy of each participant within the Prisoner’s Dilemma. Our discussion afterwards was lively, as Dr. Spindler showed how layering in mathematics to the matrix helps us predict what the participants will do. We learned about Nash equilibrium and the book, Superfreakonomics.
After learning about other ways The Prisoner Dilemma could be modeled, such as through a tree diagram, we worked on transferring our new understandings in order to build a concept of how game theory applies to a more complex problem, such as pollution or global warming. We spent time both in small groups and altogether delving into the ramifications of a particular scenario involving pollution and ultimately considered what laws might affect a situation such as this. As the workshop concluded, Dr. Spindler left us with a challenge we could work through on our own: the story of Italo Calvino, “The Black Sheep.”
Our Game Theory Workshop this week offered the opportunity to introduce new Long-View learners to a way of thinking that is crucial to our culture: we are curious people, and we set a high bar for ourselves. We know that if we invest ourselves, wonder, and work hard, we can learn about ideas and topics that are high-level, even those that are the subjects of MBA and law school classes down the street at UT, such as Game Theory.