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.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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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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