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Game Theory and the prisoner’s dilemma

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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Game Theory and the prisoner’s dilemma

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  1. Game Theory and the prisoner’s dilemma

  2. 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.

  3. 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

  4. 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!

  5. Dominant Strategy • One that is best for you, regardless of what the other party decides • In this example, the dominant strategy is to confess!

  6. Game Theory Matrix • Here is what the prisoner’s dilemma looks like written out

  7. 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.

  8. 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

  9. 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.

  10. 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

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