Essay, Research Paper: Game Theory

One of the most famous and most thoroughly studied examples of game theory is the Prisoner’s Dilemma. In this situation, the police have caught two people and charged them with a crime. The police separate the prisoners into different rooms and give them the option of confessing. The police tell the two prisoners that they have enough evidence of the crime to send them to jail for X amount of years. However, if one prisoner confesses fully to the crime and testifies against the other but the other doesn’t, then the prisoner who confessed will get get a much lighter sentence than X and the prisoner who did not confess will get a heavier sentence than X. However, if both of the prisoners confess and testify against the other, then the police have enough evidence to convict both prisoners for a slightly heavier sentence than X. Since neither of these prisoners knows what the other one is saying, we can use a decision tree to determine the dominant strategy for these people. (see figure A on attached sheet) In this dilemma, the dominant game strategy for the prisoners is to confess.
Although the strategy for these games seems very predictable, there is a paradox that arises. The police are also a player in this game. The police have evidence to put these criminals away for only X years but if the prisoners confess, then they have enough evidence to put them away for slightly more than X years. In this situation, the police want to do all they can in their power to make these criminals confess to the crime. The actions by the authorities have to be included in the outcome of the game. The way the authorities can change the outcome of the game is to penalize the prisoners if they do not do what the authorities want. Therefore the only two actions that the authority can perform are to penalize or not penalize the prisoners. However, the dominant strategy of the authority and the impact of their actions are determined by two more stipulations.
The actions of the authority and the prisoners is affected by the benevolence of the police and the flexibility of the police. If the police are benevolent, they will benefit from the gains of the prisoners, so they will do everything in the best interest of the two prisoners. If the police are flexible, they will make their decision on whether or not to penalize after the prisoners make their pleas. In this type of situation, the dominant strategy for the prisoners would be for both of them to confess and for the authority not to penalize the prisoners. The prisoners will still both have the dominant strategy of confessing because the likelihood of a smaller sentence is greatest. The dominant strategy of the police would be to not penalize because they are benevolent and they benefit from the gains of the prisoners. They also will not penalize because they are flexible and make their decision after the prisoners make theirs. Since the prisoners will have a dominant strategy of confessing and the police makes their decision on whether or not to penalize after the fact, given the police’s benevolent attitude, they will not penalize because the prisoners will already have confessed.
This circumstance of including the police in the game seems easily predictable and gives us the impression that the authority does not affect the game significantly. However, if we change the nature of the police, the game is altered greatly. If the police have a non-benevolent attitude, then they are no longer concerned about the status of the prisoners, rather they are concerned about the well-being of the public. In this case, the police may impose a penalty on the prisoners even if they do confess because they will be able to put the prisoners away for a longer time and keep them off the streets, thus preventing more crime. On the other extreme of benevolence is sadism. If the police were a sadistic force, then they would enforce a penalty on the prisoners no matter what the prisoners did. The course of the game would also be greatly altered if the police were not flexible. Not being flexible would allow the police to make a decision on penalizing prisoners before the prisoners make their plea. Since justice is blind, the police would have to commit to a certain action such as penalizing all prisoners who do not confess and not penalizing all those who do confess. This is very advantageous for the police because, for all rational situations, it puts a limit on the actions of the prisoners. Making a commitment also puts the police in a bad situation. If the prisoners are irrational and do not confess, then everyone loses. This brings up two very interesting economic principles.
The principle of “Rules rather than discretion” and


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