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Game Theory and the prisoner’s dilemma. Prisoner’s Dilemma. You have two choices…confess or stay silent: If you both confess, the DA will give you both a deal and you will serve 8 years.

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prisoner s dilemma
Prisoner’s Dilemma

You have two choices…confess or stay silent:

  • If you both confess, the DA will give you both a deal and you will serve 8 years.
  • If you both remain silent, the DA will convict you of the lesser crime and you will both serve 1 year in jail.
  • If one of you confesses, the DA will give you a deal and you go FREE, however, your partner will serve 20 years.
game theory
Game Theory
  • The study of how people behave in strategic situations
  • Must consider the actions of others and how they respond to your choices
  • Very useful when understanding the decisions of firms in oligopoly
prisoner s dilemma1
Prisoner’s Dilemma
  • Very important game
  • Each individual has to find their best strategy
  • Let’s look at our example:
    • If your partner confessed, what is your best option?
      • Confess as well and serve 8 years instead of 20
    • If you partner remained silent, what is your best option?
      • Confess because then you would go free rather than serve a year in prison
  • No matter what your best strategy is to confess!
dominant strategy
Dominant Strategy
  • One that is best for you, regardless of what the other party decides
  • In this example, the dominant strategy is to confess!
game theory matrix
Game Theory Matrix
  • Here is what the prisoner’s dilemma looks like written out
game theory and oligopolies
Game Theory and Oligopolies
  • Let’s say that a town only has two wells in it, one owned by Jack and one owned by Jill.
  • They are the only producers and both face a downward sloping demand curve.
  • Every Saturday Jack and Jill go to their wells, and decide whether to pump 30 or 40 gallons to bring into town to sell.
game theory and oligopolies1
Game Theory and Oligopolies
  • If they both produce 40 gallons to bring to market, they both get a profit of $1,600.
  • If they both produce 30 gallons, they make a profit of $1,800.
  • By lowering the quantity available, they can keep the price high.
  • However, if one sells 40 and the other sells 30, the make different amounts of money.
    • The one selling 40 makes $2,000 and the one selling 30 makes $1,500.
  • Let’s put this into a matric like the one for the prisoner’s dilemma
game theory and oligopoly
Game Theory and Oligopoly
  • We just took the idea of the prisoner’s dilemma and used it with a company to analyze profit.
  • Game Theory can lead to cooperation among companies and prisoner’s alike.
  • Playing games more than once allows companies to get better at cooperating.
  • You can enact a penalty the second time around.
nash equilibrium
Nash Equilibrium
  • When the parties in a game each choose their best strategy given the strategies that others have chosen.
  • Neither member has a reason to change their decision