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Seen in many American Tv-series

Prisoner’s dilemma

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Prisoner’s dilemma2 bad guys, each in a separate room,Being interviewed by the most

popular cops in the seriesEach prisoner being pressured to

‘snitch’ on the otherThe one who talks first gets a plea

bargainIf the other confesses first, the one

who does not confess is ‘fried’If they both confess the deal is not as

favourable

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Prisoner’s dilemma

Incomplete or

asymmetric information

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An example• The prisoners killed someone, but if they both deny

this they can only be charged for weapon possession, as nothing links them to the murder.

• Pay-off matrixprisoner 2

confessesprisoner 2

denies

prisoner 1 confesses 5 years / 5 years 0 year / 10 years

prisoner 1 denies 10 years / 0 year 1 year / 1 year

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The pay-off matrix explained• Each prisoner will receive a jail sentence of 1 year if

they both deny the charge (1 year / 1 year).

• If they both confess, they will each receive a sentence of five years (5 years/ 5 years).

• If prisoner 1 confesses and prisoner 2 denies, prisoner 1 will be offered protected custody and he will not face a jail sentence. Prisoner 2 will receive a 10 year sentence (0 year / 10 years)

• Vice versa if prisoner 1 denies and prisoner 2 confesses (10 years / 0 year).

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Nash Equilibrium

None of the participants has an interest in changing strategy because the players are playing a best response to each other.

A Nash equilibrium is not necessarily the most desirable outcome (Pareto optimum) for any or all of the participants.

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Credible threat If one of the prisoners is convinced the other will kill

him, he might make a different decision.

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Prisoner’s dilemma and cartel agreements

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Case Study : Soft and Pep

Pep blows the whistle

Pep doesn’t talk

Soft blows the whistle

€ 35 million / € 35 million € 0 / € 50 million

Soft doesn’t talk € 50 million / € 0 € 10 million / € 10 million

Pay-off matrix

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Case Study : Soft and Pep (continued)

Pep blows the whistle

Pep doesn’t talk

Soft blows the whistle

€ 35 million € 0

Soft doesn’t talk € 50 million € 10 million

Pay-off matrix Soft

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Case study : Soft and Pep (continued)If Pep blows the whistle, Soft is also better off

blowing the whistle. The fine will be €35 million instead of €50 million.

If Pep doesn’t talk, Soft will still be better off blowing the whistle. The fine will then be 0 compared to €10 million.

No matter what Pep decides, Soft is always better off by blowing the whistle.

The same applies for Pep. This is a Nash equilibrium because both Soft and Pep will blow the whistle and receive a €35 million fine each, which is not the best result for either party.