Prisoner's Dilemma

Prisoners' dilemma

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There are two prisoners whose aim is to minimize the years of imprisonment. They have committed a crime jointly. Each prisoner is interviewed separately and there are not any contacts whatsoever between them. They decide individually to confess or deny the crime taking into account possible decisions of the other prisoner (strategic game). Each prisoner chooses his dominant strategy, that is the behaviour giving the best result regardless of the decision of the other prisoner.

prisoner A

confess deny

prisoner B confess deny 3 3 1 4 4 1 2 2

The first number shows the years imprisonment of A, the second number of B. If for example A confesses and B denies, A gets 1 year imprisonment and B 4 years (field at the top right).

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Basic terms

• • • • Players: Strategy: Pay-off: Dominant strategy: decision makers ("prisoner A or B") behaviour of the players ("confess"/"deny") outcome (x years inmprisonment) the best outcome for a player regardless of the decision of the other player

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15th April 2010

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Which are the dominant strategies in this game?

from the point of view of prisoner A • • è if B confesses, I should also confess (3 years are less than 4 years) if B denies, I should again confess (1 year is less than 2 years) strategy of A: I confess irrespective of the decision of B. "Confess" ist the dominant strategy of A (3 years imprisonment).

from the point of view of prisoner B • • è if A confesses, I should also confess (3 years are less than 4 years) if B denies, I should again confess (1 year is less than 2 years) strategy of B: "Confess" is his dominant strategy, too (3 years imprisonment).

Remarks: If both prisoners could cooperate successfully, they would get a better outcome for both (2 years imprisonment). But they cannot cooperate, thus, the dominant strategy is the best result which can be achieved when deciding individually. That is the dilemma of the prisoners: By cooperation they could get a better...