Page 623 - Microeconomics, Fourth Edition

c14gametheoryandstrategicbehavior.qxd 8/6/10 8:22 AM Page 597

PROBLEMS 597

REVIEW QUESTIONS

1. What is a Nash equilibrium? Why would strategies 6. What is the difference between a pure strategy and a
that do not constitute a Nash equilibrium be an unlikely mixed strategy?
outcome of a game?
7. How can cooperation emerge in the infinitely re-
2. What is special about the prisoners’ dilemma game? Is peated prisoners’ dilemma game even though in a single-
every game presented in this chapter a prisoners’ dilemma? shot prisoners’ dilemma, noncooperation is a dominant
3. What is the difference between a dominant strategy strategy?
and a dominated strategy? Why would a player in a game 8. What are the conditions that enhance the likelihood
be unlikely to choose a dominated strategy? of a cooperative outcome in a repeated prisoners’
4. What is special about the game of Chicken? How dilemma game?
does the game of Chicken differ from the prisoners’ 9. What is the difference between a simultaneous-
dilemma game? move game and a sequential-move game?
5. Can a game have a Nash equilibrium even though 10. What is a strategic move? Why must strategic
neither player has a dominant strategy? Can a game have moves be hard to reverse in order to have strategic value?
a Nash equilibrium even though neither player has a
dominated strategy?

PROBLEMS

14.1. What is the Nash equilibrium in the following whether to follow an aggressive advertising strategy, in
game? which the firm significantly increases its spending on
media and billboard advertising over last year’s level, or a
Player 2 restrained strategy, in which the firm keeps its advertis-
Left Right ing spending equal to last year’s level. The profits associ-
Up 2, 6 8, 5 ated with each strategy are as follows:
Player 1
Down 0, 9 12, 3 Pepsi
Aggressive Restrained
14.2. Ignoring mixed strategies, does the following
game have a Nash equilibrium? Does it have more than Coca-Cola Aggressive $100, $80 $170, $40
one Nash equilibrium? If so, what are they? Restrained $80, $140 $120, $100
Player 2
What is the Nash equilibrium in this game? Is this game
West East
an example of the prisoners’ dilemma?
North 2, 1 1000, 900
Player 1 14.5. In the Castorian Airline market there are only
South 3, 2 2, 1
two firms. Each firm is deciding whether to offer a fre-
quent flyer program. The annual profits (in millions of
14.3. Does either player in the following game have a dollars) associated with each strategy are summarized in
dominant strategy? If so, identify it. Does either player the following table (where the first number is the payoff
have a dominated strategy? If so, identify it. What is the to Airline A and the second to Airline B):
Nash equilibrium in this game?
Player 2 Airline B
Left Middle Right With Frequent No Frequent
Flyer Program Flyer Program
Up 15, 12 14, 8 8, 10
Player 1 With Frequent
Down 13, 11 12, 9 5, 14 200, 160 340, 80
Airline A Flyer Program
14.4. Coca-Cola and Pepsi are competing in the No Frequent 160, 280 240, 200
Brazilian soft-drink market. Each firm is deciding Flyer Program