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Triwizard Tournament through Game Theory’s Lens

Every child understands what games are. When someone overreacts, we sometimes say “it’s just a game.” Games are often not serious… unless it involves your favorite character in Harry Potter. Today, we’ll see an example of game theory in the infamous series of Harry Potter.

Spoilers ahead!

In Harry Potter and the Goblet of Fire, we see much cooperation between Harry and the other players during the Triwizard Tournament. One specific example of this is the exchange of information between Harry and Cedric. Thanks to Hagrid, the Hogwarts gamekeeper, Harry learns that the first task will involve facing a dragon. Hagrid brings the Beauxbatons headmistress into the forest to see the dragons, and Harry runs into the Durmstrang headmaster as he is sneaking back to the castle. This leads Harry to assume that both Fleur and Krum, the other competitors in the tournament, will know about the task ahead of time. Then, Cedric, it is assumed, is the only competitor who doesn’t know what is coming.

In this “game,” the players are Harry and Cedric. We will exclude all other characters and champions for simplicity sake. Harry could have kept the information of the first task to himself, which would have given him a huge advantage over Cedric. However, Harry’s payoff in this situation is not the prize money for winning the tournament which he wasn’t interested in participating in. Rather, his decision to inform Cedric is motivated by his sense of fairness and tendency to do what he thinks is right regardless of the rules. His decision is a form of cooperation. While Harry likely was not thinking about the situation explicitly in terms of “If I help Cedric now, he’ll feel obligated to help me later,” Harry tends to make decisions based on what he perceives to be fair – this leads to him making the decision to inform Cedric. Harry is fueled by a sense of good, and throughout the series defines his personal payoff as the fulfillment of what is right, not what is profitable. If we then evaluate his decision through a lens of decency rather than profitability, it makes sense that telling Cedric has the greater personal payoff for Harry. Although Harry’s outcomes cannot be quantified easily, his desire to do the right thing is still a very real motivation.

The fact that Cedric is the other Hogwarts champion could also have played a role in this decision. Because he did not even want to enter, Harry does not care much about winning. It only makes sense that he would be rooting for the other Hogwarts champion to win if he doesn’t. Additionally, the fact that they are both from Hogwarts and have generally been on good terms in the past could have increased the trust between them, which is essential for cooperation to take place. Furthermore, Harry’s decision to tell Cedric creates an alliance between them which we see play out well for both Harry and Cedric in the second task of the tournament.

Hogwarts Alliance between Harry and Cedric. Krum and Fleur are the other participants of the Triwizard Tournament.

Cedric is the first to learn how to decipher the clue of the second task. He explicitly states that he gives Harry a hint because he feels obligated to return the favor from the previous task, so it is clear that in this case, Harry’s previous cooperation paid off greatly for him. The payoff for Cedric is the sense of doing what is right, and thus his actions are fueled by the payoff of moral satisfaction.

This is also an example of single Nash equilibrium; it seems natural to predict that Harry would want to help Cedric, given they are both from the same school and are on good terms. Similarly, because Harry told Cedric about the first task, Cedric would want to repay Harry by telling him how to decipher the clue of the second task as well. 

Game theory is widely applied in many different fields to get the best outcome for a problem. However, it is fascinating to see examples of it in a world of the fantastic. By viewing these characters’ actions through a game theory lens, we can more reasonably understand their motivations, furthering the reader’s empathy for Rowling’s creation.

Sources: https://blogs.cornell.edu/info2040/2017/09/14/harry-potter-and-the-application-of-game-theory/ https://www.maa.org/sites/default/files/pdf/ebooks/GTE_sample.pdf https://sophia.stkate.edu/cgi/viewcontent.cgi?referer=&httpsredir=1&article=1078&context=undergraduate_research_symposium

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Sentimental Analysis of Facebook users from Kashmir versus Delhi

Emotions play an important role in the way people behave, and can be affected by social or physical factors. Therefore, it is very likely that people living in the same region express varying emotions from the people living in a different region. A huge amount of data suggests that people living in “politically disturbed regions” may be subject to mental distress.

A research done at Central University, New Delhi, analyzes emotions shared on social media platforms by netizens in conflicting versus non-conflicting areas. Since most people in India use Facebook for their social activities, researchers chose this platform to collect and compare data from users living in Kashmir (a conflicting region) and Delhi (non-conflicting region). Kashmir has been recorded as a conflicting area of India, whereas Delhi has been reported as the third happiest city in India.

The researchers used Plutchik’s eight basic emotions, namely fear, anger, sadness, joy, surprise, disgust, trust and anticipation, to determine the emotional state of a user. The emotions “fear, anger, sadness and disgust” are associated with negative sentiments, whereas “joy, trust and anticipation” fall under positive sentiments. The surprise category holds the words of mixed sentiments, such as shocking and amazing.

The researchers evaluated the data to study the difference in emotions expressed by the users of the two regions. It can be observed from the scatter plot shown below that the negative emotion categories like fear, anger, and sadness contain more Kashmiri users than the Delhiites, whereas joy (a positive emotion) category contains more Delhiites. However, positive emotions such as trust and anticipation are experienced  by users from both regions.

Distribution of user emotions of Delhi Vs Kashmir regions.

In the plot, we see that trust and anticipation are expressed by both Kashmiris and Delhiites. If we were to connect the emotion “trust” to Kashmiris and to Delhiites, we will notice that both netizens have a strong connection with the emotion. Therefore, by Strong Triadic Closure property, we can conclude that Kashmiris and Delhiites have at least a weak edge between them. This can be justified because not many people from Delhi know residents of Kashmir. Therefore, it is safe to conclude that citizens of both Delhi and Kashmir won’t feel empathy towards each other.

There is a weak edge between Kashmiris and Delhiites because of Strong Triadic Closure property.

Furthermore, from the scatter plot, we see that users from Kashmir have a strong connection to negative sentiments, and users from Delhi have a stronger connection to positive sentiments. We can, therefore, cluster citizens of Kashmir and citizens of Delhi together because of the emotional connection they have between them.

This isn’t surprising because the users of the same region should experience the same emotions, in general. Since Kashmir is under siege for years, and the residents of Kashmir are regularly subjected to direct or indirect violence such as bloodshed, death, deprivation of good quality life and imposition of restrictions, they experience negative sentiments like anger and sadness. Delhiites, however, experience positive sentiments like joy. Both groups of netizens are hopeful, but in different ways. Kashmiris hope that the siege ends soon, whereas Delhiites are hopeful about their own future, rather than the city’s future.

The analysis done using the data collected, researchers found that the psychology of the citizens has been abysmally affected by the violence in the conflicting regions. They found that users in Kashmir fall under 4 negative emotion categories: fear, anger, sadness and disgust, whereas positive emotions like joy were found more in the posts made by users from Delhi.

Source: https://www.sciencedirect.com/science/article/abs/pii/S0736585318308402#f0010