The Prisoners’ Dilemma

Prisoners’ Dilemma is an application of game theory analysis in which two prisoners both confess to a crime to avoid harsher punishment when not confessing would avoid any punishment. The dilemma emerges because both prisoners are faced with the same choice – confess or not confess – but the outcome of their choice depends on the choice made by the other prisoner.
Unfortunately neither prisoner knows the choice of the other. If neither confesses, then they receive no punishment. If both confess, then they receive limited punishment, such as a year in jail. However, if one confesses and the other doesn't, the confessor receives light punishment, such as six months in jail, and the non confessor receives more severe punishment, such as five years in jail. The result is that both prisoners confess.

The model of prisoner’s dilemma explains how rivals behaving selfishly act contrary to their mutual or common interest. Wee first explain prisoner’s dilemma with an example given originally while propounding this model.

Let us suppose two persons, Ram and Hari have been caught for committing a bank robbery. Further suppose the prosecution has no enough evidence for their committing the crime. In order to obtain confession from them, they are interrogated in two separate rooms so that they cannot communicate with each other. While interrogating each accused, the police offer to Ram “If you confess to the crime (that is, cooperate with the police) while the other keeps silent (i.e. does not confess), you will be given imprisonment for only a short period, say, 1 year only but punish the other with 10 years imprisonment. If the other also confesses, the both of you would be sentenced to jail for 5 years”. It may however be known that if both prisoners do not confess, each can be jailed only for two years. The choices open to each accused are presented in payoff matrix given in the table and this refers to years of imprisonment.

Prisoner’s Dilemma: Payofff Matrix
                                                   Hari’s Choice
                                                   Confess                    Doesn’t confess
Ram’s Choice  Confesses            Hari   :     5 years      Hari   :     10 years
                                                   Ram  :    5 years       Ram   :      1 year
                       Doesn’t Confess  Hari   :    1 years       Hari    :      2 years
                                                  Ram   :    10 years     Ram   :       2 years

It will be seen that the outcome (i.e. length of sentence to each is determined by the specific strategy, (that is, choice) adopted by each prisoner. The two strategies (choices) refer to (i) confess and (ii) and does not confess. If both Hari and Ram confess, each gets 5 years imprisonment. If one confesses, but the other does not, the one who confesses (i.e. cooperate with the police) gets a very light punishment, namely imprisonment for 1 year only and the one who doesn't confess is sentenced for 10 years imprisonment. It will be further seen from the table that if both do not confess (that is, they remain loyal and faithful to each other and do not cooperate with the police), both are sentenced to 2 years imprisonment.

Now, each prisoner faces an uncertainty regarding how the other person will behave, that is, whether or not he will confess. Though each person has to make an independent choice whether to confess or not but the outcome, i.e. payoff depends on what the other does.

Now, under these circumstances what choice will be made by the prisoners when they cannot communicate with each other and have to choose between the two alternatives independently? The model of prisoners’ dilemma suggests that both behaving selfishly and working in self-interest confess to the crime and cheat each other. Since both confess, each will get imprisonment for 5 years. Why do they make this choice and confess can be shown as under. Take Hari first, most probably, he would confess when he does not know how his co-accused will act. Ram would reason like this: If I don’t confess it is very likely that I will be imprisoned for 10 years as the other prisoner will most probably confess. If I confess, I will get 5 years imprisonment if the other one also confesses and only one year imprisonment if he does not confess.

So, in the presence of uncertainty about the other person’s choice, and behaving in self-interest, Hari is likely to confess. Ram too reasoning similarly would confess. As a result, both prisoners would be sentenced for 5 years, though they would have received a lighter sentence of only two years if they had not confessed and remained loyal to each other. However, it is self-interest which leads each prisoner to confess and prevents them from attaining the best solution for themselves (2 years imprisonment) if both do not confess to the crime and remain loyal to each other. But the decision of each prisoner in favor of confession is quite rational because each person works in self-interest and tries to make the best “best” of the “worst outcomes” in an uncertain situation.

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