Game Theory: The Triwizard Tournament in Harry Potter
Game theory is widely applied in the real world, from economics to sports to military strategies, and even to famous science fiction novels. Specifically, we can find game theory being applied even in Harry Potter and the Goblet of Fire. The book revolves around The Triwizard Tournament—a tradition where the three wizard schools, Hogwarts, Beauxbatons, Durmstrang, gather to compete. At every tournament, the Goblet of Fire chooses a student representative to compete in the tournament. However, the goblet is bewitched and chooses Harry Potter in addition to the three representatives to participate in the tournament—Cedric Diggory for Hogwarts, Fleur Delacour for Beauxbatons, and Viktor Krum for Durmstrang. All four contestants must compete in three difficult tasks, all of which involve countless decisions that can be analyzed from the perspective of game theory.
Although they all compete to become the Triwizard champion, the four contestants are ultimately young students with good intentions. This leads to many scenes of cooperation amongst the four. In particular, Hagrid (Hogwarts gamekeeper) reveals to Harry what their first task will be—battling a dragon. Since Hagrid brings the Beauxbatons headmistress to see the dragons and Harry collides with the Durmstrang headmaster, Harry is aware that the only contestant absent of the information before the competition is Cedric. So, Harry is faced with the decision of either telling Cedric about the dragons or not.
For this game, we can ignore all other characters and forces, including the other two champions and Voldemort controlling the competition from afar. Thus, the two players in this game are Harry and Cedric. Although the outcomes of this game are not easily quantifiable, we can still analyze the game in descriptive payoffs.
Harry’s two strategies in this game are either not telling Cedric to acquire a significant advantage over him or telling him to ensure fairness in competition but suffer a slight disadvantage. Harry eventually makes the decision to tell Cedric about the dragons, making this situation a cooperation game. In this case, his payoff is not the monetary prize or fame of becoming the champion since he did not wish to enter anyway, but rather his overpowering desire for fairness and tendency to help others in spite of potentially losing his advantage. Later, Cedric actually discovers their second task and is also faced with the same choices of either telling Harry or not. Ultimately, he told Harry as a returning favor for telling him the previous task.
Theoretically speaking, both Harry and Cedric would want to keep their respective information to themselves as that’s their best response. They would both hope that not telling the other would increase their own advantage, resulting in a Nash Equilibrium. However, because Harry and Cedric have been on good terms and Harry revealed the first task to Cedric, they develop trust between them, leading them to cooperate to succeed in The Triwizard Tournament.
Source: https://sophia.stkate.edu/cgi/viewcontent.cgi?article=1078&context=undergraduate_research_symposium