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Prisoner's dilemma Two suspects A, B are arrested by the police.Two suspects A, B are arrested by the police. The police have insufficient evidence for a conviction, and having separated both prisoners, visit each of them and offer the same deal:The police have insufficient evidence for a conviction, and having separated both prisoners, visit each of them and offer the same deal: If one testifies for the prosecution (turns King's Evidence) against the other and the other remains silent, the silent accomplice receives the full 10-year sentence and the betrayer goes free.If one testifies for the prosecution (turns King's Evidence) against the other and the other remains silent, the silent accomplice receives the full 10-year sentence and the betrayer goes free. If both stay silent, the police can only give both prisoners 6 months for a minor charge.If both stay silent, the police can only give both prisoners 6 months for a minor charge. If both betray each other, they receive a 2-year sentence each.If both betray each other, they receive a 2-year sentence each. This can be summarized:This can be summarized: Prisoner A Stays Silent Prisoner A Stays Silent Prisoner A Betrays Prisoner B Stays Silent Prisoner B Stays Silent Bother Serve 6 months Prisoner B serves ten years; Prisoner A goes free Prisoner B Betrays Prisoner A serves ten years; Prisoner B goes free Both serve two years

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The Dilemma Each prisoner has two options:Each prisoner has two options: –to cooperate with his accomplice and stay quiet, –or to betray his accomplice and give evidence. The outcome of each choice depends on the choice of the accomplice. However, neither prisoner knows the choice of his accomplice.The outcome of each choice depends on the choice of the accomplice. However, neither prisoner knows the choice of his accomplice. The optimal solution would be for both prisoners to cooperate with each other, as this would reduce the total jail time served by the group to one year total.The optimal solution would be for both prisoners to cooperate with each other, as this would reduce the total jail time served by the group to one year total. Any other decision would be worse for the two prisoners considered together. However by each following their individual interests, the two prisoners each receive a lengthy sentence.Any other decision would be worse for the two prisoners considered together. However by each following their individual interests, the two prisoners each receive a lengthy sentence.

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Prisoner's dilemma (Corporate Setting) Two officers of the corporation – the CEO and the Comptroller are arrested for Financial Reporting fraudTwo officers of the corporation – the CEO and the Comptroller are arrested for Financial Reporting fraud The police have insufficient evidence for a conviction (they didn ’ t take my course) and having separated both prisoners, visit each of them and offer the same deal:The police have insufficient evidence for a conviction (they didn ’ t take my course) and having separated both prisoners, visit each of them and offer the same deal: If one testifies for the prosecution against the other and the other remains silent, the silent accomplice receives the full 10-year sentence and the betrayer goes free.If one testifies for the prosecution against the other and the other remains silent, the silent accomplice receives the full 10-year sentence and the betrayer goes free. If both stay silent, the police can only give both prisoners 6 months for a minor charge.If both stay silent, the police can only give both prisoners 6 months for a minor charge. If both betray each other, they receive a 2-year sentence each.If both betray each other, they receive a 2-year sentence each. This can be summarized:This can be summarized: Comptroller CooperatesComptroller Betrays CEO Cooperates-.5,-.50,-10 CEO Betrays-10,0-2,-2

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The Deal (another view) Or stated differentlyOr stated differently –Here is how the deal will look to the CEO and the Comptroller Comptroller CooperatesComptroller Betrays CEO CooperatesWin-winWin much – lose much CEO BetraysLose much – win muchLose - lose

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The Deal Or stated differentlyOr stated differently –Here is how the deal will look to the CEO and the Comptroller Comptroller CooperatesComptroller Betrays CEO Cooperates Cooperation, 6 months each Comptroller Temptation to Defect payoff of zero years CEO Betrays CEO Temptation to Defect payoff of zero yearsSucker’s Payoff (two years each)

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Why Ethics are Important! The prisoner's dilemma is a type of non-zero-sum gameThe prisoner's dilemma is a type of non-zero-sum game –it is assumed that each individual player ("prisoner") is trying to maximize his own advantage, without concern for the well-being of the other players. In Econo-speak: The Nash equilibrium for this type of game does not lead to Pareto optimums (jointly optimum solutions)In Econo-speak: The Nash equilibrium for this type of game does not lead to Pareto optimums (jointly optimum solutions) Each side has an individual incentive to cheat even after promising to cooperate. This is the heart of the dilemma.Each side has an individual incentive to cheat even after promising to cooperate. This is the heart of the dilemma. In the iterated prisoner's dilemma the game is played repeatedly.In the iterated prisoner's dilemma the game is played repeatedly. –Thus each player has an opportunity to "punish" the other player for previous non- cooperative play. –Cooperation may then arise as an equilibrium outcome. – The incentive to cheat may then be overcome by the threat of punishment, leading to the possibility of a superior, cooperative outcome. As the number of iterations approach infinity, the Nash equilibrium tends to the Pareto Optimum, because when you face eternity the threat of grudges is a grave one indeedAs the number of iterations approach infinity, the Nash equilibrium tends to the Pareto Optimum, because when you face eternity the threat of grudges is a grave one indeed

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Chapter 6 Game Theory © 2006 Thomson Learning/South-Western.

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