Step 2: Submit here when finished. The classic prisoner\'s dilemma involves two

Question

Step 2: Submit here when finished.

The classic prisoner's dilemma involves two suspects, A and B, who are arrested by the police. Because the police have insufficient evidence for conviction on a key charge, they place the prisoners in isolation and offer each of them the following deal: If one testifies for the prosecution against the other and the other remains silent, the betrayer goes free and the silent accomplice receives a 20-year sentence. If both stay silent, both prisoners are sentenced to only six months in jail on a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must make the choice of whether to betray the other or to remain silent. Neither prisoner knows for sure what choice the other prisoner will make. The dilemma is summarized as follows:







Prisoner B Stays Silent



Prisoner B Betrays




Prisoner A Stays Silent



Each gets six months



Prisoner A gets 20 years
Prisoner B goes free




Prisoner A Betrays



Prisoner A goes free
Prisoner B gets 20 years



Each gets 5 years







A.Describe the best strategy for each prisoner if neither knows what the other will do.




B.What is the paradox of the situation?

Explanation / Answer

The dominant strategy for both prisoners is to testify (and so it is a Nash equilibrium). No matter what the other person does, each prisoner is better off if he testifies. The paradox is that both would be better off mutually if they both didn't testify. But since both know that whatever the other player does, they are better of testifying they do not reach that mutual strategy. This is a very popular game theory topic as it describes situations and behaviors in business cartels. Two parties are mutually better off if they cooperate, but they don't because each one knows if the other one is going to cooperate he is better off by not cooperating.

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