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Consider a two-player game between Child's Play and Kid's Corner, each of which produces and sells swing sets for children. Each player can set either a high or a low price for a standard two-swing, one-slide set. If they both set a high price, each receives profits of $64,000 per year. If one sets a low price and the other sets a high price, the low-price firm earns profits of $72,000 per year, while the high-price firm earns $20,000. If they both set a low price, each receives profits of $57,000. Assume also that the annual discount rate is r = 25%, or d = 0.8. The price-setting game in each year could be represented in the following normal form: CP (row)/ KC (column) High Price Low Price Game between CP and KC High Price 64, 64 72, 20 Low Price 20, 72 57, 57 a) What is the stage equilibrium of the prisoners' dilemma between CP and KC? i.(L,H) ii. (H,L) iii. (L,L) iiii. (H,H) b) What is the cooperative strategy profile? i.(L,H) ii. (H,L) iii. (L,L) iiii. (H,H) c) Suppose we repeated the prisoners' dilemma between CP and KC 4 times. True or false?The players could successfully sustain cooperation in a subgame-perfect Nash equilibrium using grim trigger strategies.

Consider a two-player game between Child's Play and Kid's Corner, each of which produces and sells swing sets for children. Each player can set either a high or a low price for a standard two-swing, one-slide set. If they both set a high price, each receives profits of $64,000 per year. If one sets a low price and the other sets a high price, the low-price firm earns profits of $72,000 per year, while the high-price firm earns $20,000. If they both set a low price, each receives profits of $57,000. Assume also that the annual discount rate is r = 25%, or d = 0.8. The price-setting game in each year could be represented in the following normal form: CP (row)/ KC (column) High Price Low Price Game between CP and KC High Price 64, 64 72, 20 Low Price 20, 72 57, 57 a) What is the stage equilibrium of the prisoners' dilemma between CP and KC? i.(L,H) ii. (H,L) iii. (L,L) iiii. (H,H) b) What is the cooperative strategy profile? i.(L,H) ii. (H,L) iii. (L,L) iiii. (H,H) c) Suppose we repeated the prisoners' dilemma between CP and KC 4 times. True or false?The players could successfully sustain cooperation in a subgame-perfect Nash equilibrium using grim trigger strategies.

Principles of Microeconomics (MindTap Course List)
Principles of Microeconomics (MindTap Course List)
8th Edition
ISBN:9781305971493
Author:N. Gregory Mankiw
Publisher:N. Gregory Mankiw
Chapter17: Oligopoly
Section: Chapter Questions
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Consider a two-player game between Child's Play and Kid's Corner, each of which produces and sells swing sets for children. Each player can set either a high or a low price for a standard two-swing, one-slide set. If they both set a high price, each receives profits of $64,000 per year. If one sets a low price and the other sets a high price, the low-price firm earns profits of $72,000 per year, while the high-price firm earns $20,000. If they both set a low price, each receives profits of $57,000. Assume also that the annual discount rate is r = 25%, or 8 = 0.8. The price-setting game in each year could be represented in the following normal form: CP (row)/ KC (column) High Price Low Price Game between CP and KC High Price 64, 64 72, 20 Low Price 20, 72 57, 57 a) What is the stage equilibrium of the prisoners' dilemma between CP and KC? i.(L,H) ii. (H,L) iii. (L,L) iiii. (H,H) b) What is the cooperative strategy profile? i.(L,H) ii. (H,L) iii. (L,L) iiii. (H,H) c) Suppose we repeated the prisoners' dilemma between CP and KC 4 times. True or false? The players could successfully sustain cooperation in a subgame-perfect Nash equilibrium using grim trigger strategies. d) Suppose that the two firms play this game infinitely many times. Define the grim strategy for each firm. i. (Cooperation/Punishment) phase: play (high/low) in the first period and as long as no defection has happened before. ii. (Cooperation/Punishment) phase: play (high/low) (for two periods/forever/for
Transcribed Image Text:Consider a two-player game between Child's Play and Kid's Corner, each of which produces and sells swing sets for children. Each player can set either a high or a low price for a standard two-swing, one-slide set. If they both set a high price, each receives profits of $64,000 per year. If one sets a low price and the other sets a high price, the low-price firm earns profits of $72,000 per year, while the high-price firm earns $20,000. If they both set a low price, each receives profits of $57,000. Assume also that the annual discount rate is r = 25%, or 8 = 0.8. The price-setting game in each year could be represented in the following normal form: CP (row)/ KC (column) High Price Low Price Game between CP and KC High Price 64, 64 72, 20 Low Price 20, 72 57, 57 a) What is the stage equilibrium of the prisoners' dilemma between CP and KC? i.(L,H) ii. (H,L) iii. (L,L) iiii. (H,H) b) What is the cooperative strategy profile? i.(L,H) ii. (H,L) iii. (L,L) iiii. (H,H) c) Suppose we repeated the prisoners' dilemma between CP and KC 4 times. True or false? The players could successfully sustain cooperation in a subgame-perfect Nash equilibrium using grim trigger strategies. d) Suppose that the two firms play this game infinitely many times. Define the grim strategy for each firm. i. (Cooperation/Punishment) phase: play (high/low) in the first period and as long as no defection has happened before. ii. (Cooperation/Punishment) phase: play (high/low) (for two periods/forever/for
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