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Wize University Microeconomics Textbook > Oligopoly

Prisoner's Dilemma

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Prisoner's Dilemma:

Prisoner's Dilemma is the most common example of Nash equilibrium. It consists of two criminals that have been caught robbing a bank and they are placed in separate cells while being questioned. Their payoff matrix (years in jail) is presented below.

Dominant Strategy for Criminal A

  • If criminal B confesses to the crime, it is better for criminal A to
    confess
    since
    6
    years is better than
    10
    years in prison
  • If criminal B denies the crime, it is better for criminal A to
    confess
    since
    0
    years is better than
    1
    year in prison
  • Therefore criminal A's dominant strategy is to
    confess

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Dominant Strategy for Criminal B

  • If criminal A confesses to the crime, it is better for criminal B to
    confess
    since
    6
    years is better than
    10
    years in prison
  • If criminal A denies the crime, it is better for criminal B to
    confess
    since
    0
    years is better than
    1
    year in prison
  • Therefore criminal B's dominant strategy is to
    confess

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Nash Equilibrium

  • The Nash equilibrium is when both criminals
    confess
    because neither player has an incentive to
    cheat
    ,
  • If we are in the top left box and criminal A cheats, he will end up doing
    10
    years in jail instead of
    6
    years in jail.
  • If we are in the top left box and criminal B cheats, he will end up doing
    10
    years in jail instead of
    6
    years in jail.
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Mutually Beneficial Outcome

  • If they were able to collude both criminals would
    deny
    the crime and each of them would do
    1
    year in jail
  • However, this outcome is not sustainable because each criminal has an incentive to
    cheat
    ,
  • If we are in the bottom right box and criminal A cheats, he would do
    0
    years in jail instead of
    1
    year.
  • If criminal B cheats. he would do
    0
    years in jail instead of
    1
    year.


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Example: Nash Equilibrium with Common Resources

Common resources like oil wells and fisheries can be overused.


a) What is the dominant Strategy for Exxon (if they have one)?
a) Dominant Strategy for Exxon: Drill 2 wells
b) What is the dominant Strategy for Texaco (if they have one)?
b) Dominant Strategy for Texaco: Drill 2 wells

c) What is the Nash equilibrium?
c) Nash Equilibrium: (2 wells, 2 wells)

d) Is there a mutually beneficial outcome compared to the Nash equilibrium?
d) Mutually Beneficial Outcome: (1 well, 1 well)