Prisoner's dilemma

1
Prisoner's dilemma

• 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
• 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 betray each other, they receive a 2-year
  sentence each.
• This can be summarized

2
The Dilemma

• 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 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.

3
Prisoner's dilemma (Corporate Setting)

• Two officers of the corporation the CEO and the
  Comptroller are arrested for Financial Reporting
  fraud
• The police have insufficient evidence for a
  conviction (they didnt 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 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.
• This can be summarized

4
The Deal (another view)

• Or stated differently
• Here is how the deal will look to the CEO and the
  Comptroller

5
The Deal

• Or stated differently
• Here is how the deal will look to the CEO and the
  Comptroller

6
Why Ethics are Important!

• The 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)
• 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.
• 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 indeed