An Aside on Game Theory

1
An Aside on Game Theory

• Study of how decision makers behave in strategic
  situations
• when each actor must consider the reactions of
  others
• Nash equilibrium is an application of game theory
• another useful application is the Prisoners
  Dilemma
• a non-cooperative game

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Prisoners Dilemma

• Police catch two criminals
• Bonnie and Clyde
• Police have enough to convict each on a minor
  charge of possession of firearms but need a
  confession to get them on bank robbery
• possession gets them each one year in jail
• Police keep each in separate rooms

3

• Police make each a deal
• confess and well go easy on you
• if both confess each gets minimum 8-year sentence
• if only one confesses AND agrees to rat on the
  other he or she will be let free and the other
  will get the maximum sentence of 20 years

4

• Will Bonnie confess or remain silent?
• if Clyde confesses, she is better off confessing
• she 8 years as opposed to 20
• if Clyde remains silent, she is better off
  confessing
• she goes free
• either way, she is better off confessing
• confessing is her dominant strategy
• Clyde has same incentives
• So both confess even though both would be better
  off remaining silent
• both get 8 years when they could have gotten off
  with only 1 year

5
Oligopoly as a Prisoners Dilemma

• We can model our Motown oligopoly as a prisoners
  dilemma
• high output is dominant strategy for both
• both would be better off with low output

6
Advertising as a Prisoners Dilemma

• The cigarette market is an oligopoly
• In 1971, Congress banned advertising
• The industry had not opposed the ban even though
  each firm was heavily advertising
• The ban solved their prisoners dilemma
• without the ban, each firms dominant strategy is
  to advertise even though each is better off not
  advertising as long as none advertises

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Advertising as a Prisoners Dilemma
8
The Arms Race as a Prisoners Dilemma
9
Common Resources

• Oil companies drilling from same pool
• Fishermen catching from same fishing ground
• Result is over-utilization of common resource

10
Common-Resource Game
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Non-Cooperation and Social Welfare

• The prisoners dilemma game can be used to model
  many real-life situations
• In some cases, society is better off with
  non-cooperation
• oligopoly
• prisoners
• In some cases, society is worse off
• arms race
• common resources