Harry Potter: From a Game Theoretic Lens
Article: https://medium.com/@nsilverblatt/game-theory-in-harry-potter-ce04907d3144
This article highlighted an example of game theory in Harry Potter, specifically occurring in Harry Potter and the Order of the Phoenix when Voldemort attempts to convince Harry to go to the Ministry of Magic in order to secure the prophecy for him. The article explores a two player game involving Harry and Voldemort and details payoffs depending on their respective strategies. As Harry Potter is one of my most beloved fictional worlds, this article inspired me to think of more potential scenarios in Harry Potter that could be explored via a game theoretic lens.
One such scenario I wanted to explore was Harry Potter’s first ever quidditch match in Harry Potter and the Philosopher’s Stone. During the quidditch match, Professor Quirrell, who is one of Voldemort’s henchmen is attempting to kill Harry by chanting a spell to throw him off his broom. Professor Quirrell is aware that there are many people in Hogwarts who wish to keep Harry Potter alive and will potentially thwart his plans. One such person is Professor Snape who is motivated by his love for Lily (Harry’s mother) to keep Harry alive even though, on a superficial level, it appears to people that he hates Harry. Additionally, in order to keep Harry alive, Snape promised Dumbledore to act as a double agent through posing as one of Voldemort’s devoted death eaters. Thus, it is important for Snape to keep his true affiliation a secret and not compromise his real identity to Voldemort or anyone else for that matter.
The two players in this game are Professor Quirrell and Professor Snape. Quirrell has the opportunity to either chant or not chant in order to try killing Harry Potter during the Quidditch game. Quirrell’s payoff for chanting and, ultimately, killing Harry Potter is the immense satisfaction of Lord Voldemort and deeming Quirrell as one of his most loyal death eaters. Conversely, not even attempting to kill Harry at every possible opportunity, such as at the Quidditch match, puts Quirrell in danger of facing Voldemort’s wrath. If Quirrell attempts to kill Harry but fails, he would still face Voldemort’s wrath but to a lesser extent. As for Snape, his payoff for saving Harry’s life is the self-satisfaction of doing what he believes is morally right to save Lily’s son and holding true to his promise to Dumbledore. However, Snape also faces a negative payoff by chanting the spell to save Harry’s life in regards to raising suspicion about whether he is actually trying to kill Harry since he was previously a death eater. If Snape chooses not to chant the spell, there is no suspicion placed on him of trying to kill Harry. However, he fails to achieve his more valuable objective of saving Harry’s life. Thus, taking these factors into consideration, we can create a payoff matrix as shown below. It is difficult to quantify these payoffs so while the numbers are arbitrary, the relative value of one payoff to another is not.
| Snape | |||
| Chant Spell | Don’t chant spell | ||
| Quirrell | Chant spell | -1, 3 | 5,-3 |
| Don’t chant spell | -4, -2 | -4,5 | |
The Nash Equilibrium for this payoff occurs when both players chant a spell with Quirrell receiving a payoff of -1 and Snape of 3. These strategies are mutual best responses and is what actually occurs in the book. Quirrell attempts to throw Harry off his broom by chanting a spell but he is foiled by Snape’s counter-spell. A negative payoff that Snape experiences, however, is Hermione setting his cloak on fire because she suspects that Snape is the one trying to kill Harry. From Quirrell’s perspective, he still experiences a negative payoff to some extent because even though he attempted to kill Harry, he was not successful which Voldemort will be displeased about. Thus, his overall payoff is -1.