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EC101 Chapter 15 Review Questions 40

1. Using your own words, please define the following words from Chapter 15 (10 pts.):
   1. Collusion

• Cooperative Equilibrium

• Dominant Strategy Equilibrium

• Duopoly

• Game Theory

• Nash Equilibrium

• Oligopoly

• Payoff Matrix

1. Strategies

• Name two characteristics of oligopolies, as discussed in class. (2 pt.)

• George and Lee are contestants on a game show where they are both asked a question, which they can choose to answer honestly or they can lie. The payoff matrix below illustrates the potential payoffs based on how each contestant answers the question. (4 pts.)

Lee

200

200

-150

250

320

100

-150

100

Lie

Lie

Truth

Truth

George

1. Does George have a dominant strategy? If so, what is it?

• Does Lee have a dominant strategy? If so, what is it?

• Is there a Nash equilibrium? If so, what is it? If there is more than one, name all the Nash equilibriums.

• Is the outcome the most optimal outcome? If not, what is the most optimal outcome?

• Ollivander and Gregorovitch are the only two firms that sell wands. Assume they agree to collude by agreeing to decrease quantity to increase prices and profit. Also assume the two firms can only change their quantity once a week. Each week, both companies have the option to comply with the agreement, or cheat. The matrix below illustrates the potential payoffs, in millions of dollars, based on the potential outcomes each week. After the first week, Ollivander lost $2 million and Gregorovitch earned $4 million. Assume that throughout the duration of the agreement, Ollivander will use a trigger strategy and Gregorovitch will use a tit-for-tat strategy (5 pts.)

Gregorovitch

$2

$2

-$2

$4

$4

$0

-$2

$0

Comply

Comply

Cheat

Cheat

Ollivander

1. What will Ollivander choose to do the second week?

• What will Gregorovitch choose to do the second week?

• What will Ollivander choose to do the third week?

• What will Gregorovitch choose to do the third week?

• What will be the outcome of the ninth week?

• Do all games result in one Nash equilibrium? (1 pt.)

• Do all games result in a dilemma? (1 pt.)

• Assume Albus and Hagrid are trying to decide where to go to dinner. Albus prefers eating at a seafood restaurant, but Hagrid prefers eating at an American restaurant. Albus receives a total utility of 8 when he eats at a seafood restaurant with Hagrid, a total utility of 2 when he eats at a seafood restaurant alone, a total utility of 5 when he eats at an American restaurant with Hagrid, and a total utility of 1 when he eats at an American restaurant alone. Hagrid receives a total utility of 7 when he eats at an American restaurant with Albus, a total utility of 2 when he eats at an American restaurant alone, a total utility of 4 when he eats at a S=seafood restaurant with Albus, and a total utility of 1 when he eats at a seafood restaurant alone. (6 pts.)

1. Assume they only plan to eat out once this month.

1. Draw the payoff matrix to show the payoffs for each possible outcome.

1. Is there a Nash equilibrium? If so, what is it? If there is more than one, name all the Nash equilibriums.

• Assume Albus and Hagrid decide to go out to eat twice; once this weekend and once next weekend. They agree that if Albus chooses the restaurant this weekend, then it’s only fair Hagrid chooses dinner the following weekend.

1. Draw the decision tree to illustrate the payoffs for each possible outcome.

1. Assume Albus will act in his own best interest. Which restaurant will he choose this weekend?

• What is the difference between a tit-for-tat strategy and a trigger strategy? (2 pts.)

• If one player has a dominant strategy in a game with two players, will there be a Nash equilibrium? (1 pt.)

1. Currently, Sirius Inc. is the only firm in the market designing and selling “Most Wanted” posters to the FBI. Currently, they sell the posters for $15 per person. However, Beatrix Corp. is considering entering the market. Sirius can either keep the price at $15, or he can drop it $10. Below is the decision tree illustrating the potential outcomes. (3 pts.)

Monopoly Price of $15

Competitive Price of $10

Stay Out

Enter

(1,000, 0)

(-3,500, -2,000)

(15,000, 0)

(-5,000, 8,000)

Sirius Inc.

Beatrix Corp.

Beatrix Corp.

Enter

Stay Out

1. If Sirius Inc. keeps the price at $15, is it a rational decision for Beatrix Corp. to enter the market?

• If Sirius Inc. drops the price at $10, is it a rational decision for Beatrix Corp. to enter the market?

• Assuming Sirius Inc. believes Beatrix Corp. will act rationally, should they keep the price at $15, or drop it to $10?

1. Assume two companies collude and agree to cut production to increase price and profit. Both companies can only adjust their output levels on the first of every month. (2 pts.)
   1. If the agreement is in place for one year, is it in either company’s best interest to cheat? If so, when should they cheat?

• If the agreement is in place forever, is it in either company’s best interest to cheat? If so, when should they cheat?

1. Harry and Draco are in a duel against each other. Unfortunately, they only remember two spells to cast: expelliarmus and stupefy. Below is the payoff matrix illustrating the points they’ll earn based on impact their spell has on their opponent when they cast spells simultaneously. (3 pts.)

Stupefy

Dracro

3

3

6

5

4

5

5

6

Stupefy

Expelliarmus

Expelliarmus

Harry

1. Does Draco have a dominant strategy? If so, what is it?

• Does Harry have a dominant strategy? If so, what is it?

• Is there a Nash equilibrium? If so, what is it? If there is more than one, name all the Nash equilibriums.

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