Game Theory

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Game Theory
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Prisoner's Dilemma

• A crime has been committed and 2 suspects have
  been arrested and put in separate rooms.
• The police make them the following offer
• If you each confess, I will send both of you to
  prison for 5 years.
• If none of you confess, I will send both of you
  to prison for 2 years.
• If your friend confess and you do not, I will
  send you to prison for 10 years and will send
  your friend to prison for 1 year.
• If you confess and your friend does not, I will
  send you to prison for 1 year and I will send
  your friend to prison for 10 years.

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• Games in Strategic Form
• Players
• Strategies
• Payoffs (costs or benefits)

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Prisoner's Dilemma
Prisoner A
Prisoner B
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The Breakdown of Collusion

• You have an exam and your professor is going to
  curve the grades. Your grade depends on how your
  grades compares to your classmates grades.
• You can get together with your classmates and
  collude not to study. If the collusion is
  successful everybody might be better off if
  studying has a cost (effort is higher than
  increased knowledge). But there are high
  incentives for a single student to cheat and
  deviate from the agreement.
• Players 2 players. You and your classmate.
• Strategies deviate from collusion agreement
  (cheat, study) or not (no cheat, no study).
• Payoffs (in this case high is good)
• If you each cheat (not respect the agreement),
  the payoff (grade minus effort) is 2 for both of
  you.
• If none of you cheat, both of you have a payoff
  of 3.
• If your friend cheats and you do not, your friend
  has a payoff of 4 and you have a payoff of 1.
• If you cheat and your friend does not, your
  friend has a payoff of 1 and you have a payoff of
  4.

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Collusion in an Exam
Student A
Student B
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Equilibrium in Strictly Dominated Strategies

• A strategy is strictly dominant for a player if
  regardless of what the other player does he or
  she will play it.
• In an equilibrium in dominant strategies both
  players play strictly dominant strategies.
• Pareto Optimality versus Equilibrium

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Pigs in a Box

• A strong and a weak pig are kept in a box. The
  box has a lever on one side and a food dispenser
  on the other. When the lever is pushed, food
  appears at the dispenser.
• If the weak pig pushes the lever, the strong pig
  waits at the dispenser and eats all the food.
• If the strong pig pushes the lever, the weak pig
  waits at the dispenser and eat part of the food.
  When the strong pig arrives at the dispenser, it
  pushes away the weak pig and eat the leftovers.
• Pushing the lever burns 10 calories and there are
  100 calories worth of food at the dispenser.

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Pigs in a Box
Does the strong pig have a Strictly Dominant
Strategy?
Strong Pig
Weak Pig
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Battle of the Sexes

• A husband prefers to go to a boxing match and his
  wife prefers to go to the opera, but they like
  doing things together.

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Battle of the Sexes
Husband
Wife
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Nash Equilibrium

• An outcome is a Nash Equilibrium if neither
  player want to deviate from it taking the
  opponent behavior as given.
• If the husband thinks that the wife is going to
  opera, he will go to the opera. If the wife
  thinks that the husband is going to the opera,
  she will go to the opera. Both players going to
  the opera is a NE. Both players going to the
  boxing game is also a NE.
• Dominant strategy equilibrium is a much stronger
  concept (regardless of what the other player
  does). An equilibrium in dominant strategies is
  always a NE but not vice versa. If a game has a
  DE equilibrium this is the only equilibrium of
  the game.

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War Game

• Two countries are deciding whether to spend their
  budget on health or defense.
• 1- If both countries spend their budget on health
  they both have an utility of 100. If they both
  spend their budget on defense they get an utility
  of 0. If one country spends the budget on health
  and the other one spends on defense, the country
  spending the money on defense gets an strategic
  advantage over the other one. Therefore, the
  country spending the money on health gets a
  payoff of -100 and the country spending the money
  on defense gets a payoff of 200.
• A)- Who are the players.
• B)- What are their strategies.
• C)- Is there an equilibrium in strictly dominated
  strategies.
• D)- Is there a Nash Equilibrium.

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War Game
Country I
Country II
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War Game

• Two countries are deciding whether to spend their
  budget on health or defense.
• 2- If both countries spend their budget on health
  they both have an utility of 100. If they both
  spend their budget on defense they get an utility
  of 1. If one country spends the budget on health
  and the other one spends on defense, both
  countries have a payoff of zero.
• A)- Who are the players.
• B)- What are their strategies.
• C)- Is there an equilibrium in strictly dominated
  strategies.
• D)- Is there a Nash Equilibrium.

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War Game
County I
Country II
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Ice-cream Sellers
Two Ice-cream sellers have to decide where to
locate on a linear beach. Both sellers charge the
same price. Consumers will buy from the nearest
seller.
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• ____ The adverse selection process is prevalent
  in the used car market because
• a.only poorer people are likely to purchase used
  cars.
• b.sellers know more about the vehicles being sold
  than do potential buyers.
• c.the price of the car sends a signal about its
  quality.
• d.so many consumers are adverse to buying used
  cars.

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• ____ When do insurance companies encounter the
  problem of moral hazard?
• a.When they do not have enough information to
  distinguish between people who are "good risks"
  and those who are "bad risks.
• b.When simply having insurance causes people to
  take more risks than they would otherwise.
• c.When the price of insurance premiums fully
  reflects all available information.
• d.When the insurance company suffers large losses
  because a major catastrophe has affected a large
  number of people simultaneously.

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• Each firm has a choice of advertising, ads, or
  not advertising, no ad. The profits each gets
  depend upon which it chooses.
• Firm A ads-Firm B ads. A gets 300, B gets 300
• Firm A no ads-Firm B no ads. A gets 500 B gets
  500
• Firm A no ads-Firm B no ads. A gets 100 B gets
  900
• Firm A ads-Firm B no ads. A gets 400 B gets 100
• ____ 1- In this game,
• a.Firm A's dominant strategy is to advertise.
• b.Firm A's dominant strategy is no to advertise.
• c.Firm B's dominant strategy is to advertise.
• d.Firm B has no dominant strategy.
• ____ 2. The Nash equilibrium is to be found where
• a.neither firm advertises.
• b.Firm A advertises, Firm B does not.
• C Firm A does not advertise but Firm B does.
• d.both firms choose to advertise.