One of the common misconceptions of The Dark Knight revolves around the boat scene. Two boats, one filled with Gotham's most notorious criminals and the other filled with citizens of Gotham, are filled with explosives by the Joker's henchmen. The Joker provides the two boats with an ultimatum: either destroy the other boat by a certain time or the Joker will destroy both boats. Often, this situation is compared to the Prisoner's Dilemma, one of the most well known and popular games in game theory. There are two prisoners who are accomplices to the other. They have two choices: either confess to the crime or stay silent. If both prisoners confess to the crime, they are sentenced to 5 years in prison. If one prisoner confesses (and thus implicates the other) but the other stays silent, the prisoner who confessed is released from custody and the prisoner who stayed silent is sentenced to 10 years. However, if neither prisoner confesses, they are sentenced to 1 year in prison. So, it would be appear that the best situation is that neither prisoner confesses. But if one prisoner stays silent, the other prisoner has the incentive to confess to the crime, relieving himself of any time in jail. Since confessing is the better option regardless of what choice the other prisoner makes, both prisoners would rationally confess, but by doing so, they end up with 5 years of prison time each as opposed to 1 year, which is the outcome they would have if they cooperated.
The fatal flaw in the comparison between the Prisoner's Dilemma and the scenario in The Dark Knight is that not all outcomes can have a payout because of the essential impossibilty of one of the outcomes. If we were to build out the game, we would see that there are 2 players (the two ships) and 2 options (blow up the other ship or do nothing). This should lead to four outcomes, but one of the outcomes is essentially impossible in the Prisoner's Dilemma game. I think that the outcome where both players decide to blow the other player up is not realistically probable (though not impossible). If you were playing this game, you would not consider both players deciding to blow the other player up as an option. Unlike the Prisoner's Dilemma, The Dark Knight ship problem introduces an element of time. So in this game, you would have 3 options: you blow the other player up, the other player blows you up, or neither player blows up the other. While the Prisoner's Dilemma may not apply, the understanding we get from that game (and game theory) does allow us to delve deeper into one of the main ideas from that movie.
If in the Prisoner's Dilemma it is always better to confess, then we should hypothesize that one of the ships should have detonated the other ship. A rational person would value their survival over their death and not detonating the other ship will always lead in one's death in this game (barring an otherworldly power like Batman). However, both sides believed that not detonating the other ship is the better option. Assume the one ship does not opt to detonate the other (I'm going to make this assumption because the situation where both ships decide to detonate at the same time is implausible). The other ship could detonate or not detonate. We see in the film that the other ship does not choose the detonation because it has the better payoff, so survival is trumped by some other cause. I theorize that a rational person would detonate the other ship, but a moral person would not. Rather than live with burden of having killed an entire ship full of people, we would die knowing that we did the right thing. This idea is reminiscent of an oft quoted line said by Harvey Dent: "You either die a hero or you live long enough to see yourself become the villain." This binary morality drives the actions of Batman, Harvey Dent (and later Two-Face), and even the people on that ship. They could have survived by killing people, taking the role as the villain. But they saw that it would be better to die, heroically standing against the Joker's maniacal game.
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