# Game Theory and the Dark Knight

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Game Theory and The Dark Knight

The most infamous Game Theory is the prisoner's dilemma. The prisoner's dilemma demonstrates how difficult the cooperative behavior can be in certain circumstances (Colander, Microeconomics 257). The Prisoner's Dilemma is presented through the payoff matrix, which is a table showing the outcome of every choice each player makes. Overall, in the Prisoner's Dilemma (illustrated in our textbook) concludes how if each of the prisoners didn't agree to confess, the result would be a light sentence for both of them (Colander, Microeconomics 258). However, the risk of not knowing whether the other prisoner will confess will lead to the result that confessing is the most rational choice for each prisoner. This choice of both of the prisoners confessing will lead to the sentencing of each of the prisoners to five years in jail. (Colander, Microeconomics 258). This solution to the Prisoner's Dilemma is the Nash Equilibrium, which is defined as the "set of strategies for each player in the game in which no player in the game can improve his/her payoff by changing strategy unilaterally". (Colander, Microeconomics 259)

In the movie, we see the city of Ghotham being evacuated. There are two ships that were filled with people. One of the ferries is filled with law-abiding citizens, including various city officials. On the other hand, the second ship is filled with the entire criminal population from Gotham's prison. The Joker has filled each of the two ships with explosives. The explosives are that powerful that if they explode, they would destroy the entire boat; killing every person on-board.

While discovering the explosives, each of the ferries discovers a detonator. Through a recorded announcement they are told that the push of the detonator would blow up the other ship, while the population of the ship pushing the detonator will be saved. For example, if ferry A pushed the detonator, ferry B would be destroyed, while the people in ferry A will be saved and vice versa. Additionally, in the recorded announcement the people in the ferries are told that if neither ship uses the detonator within half-an-hour, then both of the ferries will be destroyed by the Joker (Allen M.,2009). Considering that all the actors involved in this 'game' are making their decision simultaneously following the example of the Prisoner's Dilemma in Game Theory, the following 'game' would take place:

Figure 1: Joker's Ferry Detonator Game - Predicted Payoff

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