Applying Game Theory to Ultimate Frisbee
The topic of game theory discussed in class is applicable to many things in today’s society and it is especially prevalent in sports. I chose to explore how game theory applies to ultimate frisbee since I currently play frisbee for the Cornell Buds. This small-scale research project performed by Harvard Ph.D. student, Alex Albright, goes deep into how choosing specific players for a specific point affects the score and result of the game. Then, they explore how throwing to a female in mixed gender ultimate can be modeled as a Bayesian Equilibria. Since we haven’t covered Bayesian Equilibrium, I will mainly be discussing the first half of the research project.
Some basic context for ultimate frisbee, “each team needs to put 7 people on the line to play any given point. However, teams themselves consist of more than 7 people.” (Albright) Out of all of the people that make up a team, there will be players who have a stronger skill set and for the first “Game,” Alex “assume there are two teams, 1 and 2, that are identical and each always has two lines… a strong line and a weak line…” (Albright) Of course, in real life, there would be more lines but for simplicity’s sake, there are only two teams with two lines. Continuing with the setup of the game, winning a point yields 3 points, losing a point loses 3 points, and if two types of the same lines are played, they receive 0. Additionally, there is an additional price of 1 point to play a strong line and teams actually get a point if they play a weak line. Although not explicitly stated in the description, I am assuming that both teams will be playing their lines at the exact same time so that no team has an advantage in line calling. The payoff is summarized in the matrix below.
This is a pretty simple Prisoner’s Dilemma question that we have covered in class and in fact, there is a pure Nash equilibrium of playing the strong lines for both teams. However, it is important to note that if both teams play their weak lines, they actually both benefit the most.
After this basic example, Alex decides to more accurately model how ultimate line calling by adding offense and defense since there may be players who are better at either role. The payoffs of playing strong and weak lines are summarized below in another payoff matrix.
We can see that there are no pure Nash equilibriums but, there is indeed a mixed Nash equilibrium which is Team 1 playing a weak line with probability 2/3 and a strong line with probability 1/3 while Team 2 plays the weak line with probability 1/3 and their strong line with 2/3 probability. (Albright)
It is really interesting to see the widespread influence of game theory in our daily lives and the next time my team goes to a tournament, I will be keeping this in the back of my mind.
https://thelittledataset.com/2017/01/09/ultimate-game-theory/