Consider the following Bertrand Duopoly game between Firm A and Firm B. Firm B Bertrand Duopoly Low Price High Price Low Price 0,0 5,-1 Firm A High Price -1,5 3,3 a. Is there a dominant strategy equilibrium for a one-shot, simultaneous-move game? If so, what is it? If not, explain why. (2 points) b. Identify any and all Nash equilibria for a one-shot, simultaneous-move game. (1 point) c. What is Firm A's secure strategy for a one-shot, simultaneous-move game? What is Firm B's secure strategy for a one-shot, simultaneous-move game? (2 points) d. Assume that Firm A and Firm B agree to collude and both charge high prices as long as neither of them cheats by charging low prices. If one of the firms cheats, trigger strategies take hold whereby the "victim" punishes the "cheater" by charging low prices forever after. If this game is infinitely repeated, calculate the interest rate (i) necessary to sustain collusion. (3 points) e. Assume that Firm A and Firm B agree to collude and both charge high prices as long as neither of them cheats by charging low prices. If one of the firms cheats, trigger strategies take hold whereby the "victim" punishes the "cheater" by charging low prices thereafter. If this game is finitely repeated with an unknown final period, assuming that the interest rate is 0%, calculate the probability that the game will end after a given play (0) necessary to sustain collusion. (2 points)
Consider the following Bertrand Duopoly game between Firm A and Firm B. Firm B Bertrand Duopoly Low Price High Price Low Price 0,0 5,-1 Firm A High Price -1,5 3,3 a. Is there a dominant strategy equilibrium for a one-shot, simultaneous-move game? If so, what is it? If not, explain why. (2 points) b. Identify any and all Nash equilibria for a one-shot, simultaneous-move game. (1 point) c. What is Firm A's secure strategy for a one-shot, simultaneous-move game? What is Firm B's secure strategy for a one-shot, simultaneous-move game? (2 points) d. Assume that Firm A and Firm B agree to collude and both charge high prices as long as neither of them cheats by charging low prices. If one of the firms cheats, trigger strategies take hold whereby the "victim" punishes the "cheater" by charging low prices forever after. If this game is infinitely repeated, calculate the interest rate (i) necessary to sustain collusion. (3 points) e. Assume that Firm A and Firm B agree to collude and both charge high prices as long as neither of them cheats by charging low prices. If one of the firms cheats, trigger strategies take hold whereby the "victim" punishes the "cheater" by charging low prices thereafter. If this game is finitely repeated with an unknown final period, assuming that the interest rate is 0%, calculate the probability that the game will end after a given play (0) necessary to sustain collusion. (2 points)
Principles of Microeconomics (MindTap Course List)
8th Edition
ISBN:9781305971493
Author:N. Gregory Mankiw
Publisher:N. Gregory Mankiw
Chapter17: Oligopoly
Section: Chapter Questions
Problem 9PA
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Question
Transcribed Image Text:Consider the following Bertrand Duopoly game between Firm A and Firm B.
Firm B
Bertrand Duopoly
Low Price
High Price
Low Price
0,0
5,-1
Firm A
High Price
-1,5
3,3
a. Is there a dominant strategy equilibrium for a one-shot, simultaneous-move
game? If so, what is it? If not, explain why. (2 points)
b. Identify any and all Nash equilibria for a one-shot, simultaneous-move game. (1
point)
c. What is Firm A's secure strategy for a one-shot, simultaneous-move game? What
is Firm B's secure strategy for a one-shot, simultaneous-move game? (2 points)
d. Assume that Firm A and Firm B agree to collude and both charge high prices as
long as neither of them cheats by charging low prices. If one of the firms cheats,
trigger strategies take hold whereby the "victim" punishes the "cheater" by charging
low prices forever after. If this game is infinitely repeated, calculate the interest
rate (i) necessary to sustain collusion. (3 points)
e. Assume that Firm A and Firm B agree to collude and both charge high prices as
long as neither of them cheats by charging low prices. If one of the firms cheats,
trigger strategies take hold whereby the "victim" punishes the "cheater" by charging
low prices thereafter. If this game is finitely repeated with an unknown final period,
assuming that the interest rate is 0%, calculate the probability that the game will
end after a given play (0) necessary to sustain collusion. (2 points)
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