1. Consider the following interaction between a single long lived firm, and a sequence of short-lived consumer. In each period t = 1, 2.….., there is a single consumer who only lives for one period. The consumer must choose between the actions BUY and NOT BUY (i.e. B and N). The firm must chooose what quality level to provide, i.e. it must choose between H and L. The payoffs to the two parties are given by the following table, where Ví > p > v₁ and p > CH > CL- H L VH-P₂P-CH VL-P, P-CL 0,0 В N 0,0 a) Solve for the Nash equilibria of the above stage game. b) Suppose that the firm discounts payoffs at rate d, where 0 < d < 1. Each consumer at date t observes the actions of the firm and of previous consumers in all previous periods, 1, 2..., t – 1. Show that there exists a sub- game perfect equilibrium where the firm provides high quality, if & is large enough. (Hint: construct a trigger strategy equilibrium).
1. Consider the following interaction between a single long lived firm, and a sequence of short-lived consumer. In each period t = 1, 2.….., there is a single consumer who only lives for one period. The consumer must choose between the actions BUY and NOT BUY (i.e. B and N). The firm must chooose what quality level to provide, i.e. it must choose between H and L. The payoffs to the two parties are given by the following table, where Ví > p > v₁ and p > CH > CL- H L VH-P₂P-CH VL-P, P-CL 0,0 В N 0,0 a) Solve for the Nash equilibria of the above stage game. b) Suppose that the firm discounts payoffs at rate d, where 0 < d < 1. Each consumer at date t observes the actions of the firm and of previous consumers in all previous periods, 1, 2..., t – 1. Show that there exists a sub- game perfect equilibrium where the firm provides high quality, if & is large enough. (Hint: construct a trigger strategy equilibrium).
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:1. Consider the following interaction between a single long lived firm,
and a sequence of short-lived consumer. In each period t = 1,2..., there is a
single consumer who only lives for one period. The consumer must choose
between the actions BUY and NOT BUY (i.e. B and N). The firm must
chooose what quality level to provide, i.e. it must choose between H and
L. The payoffs to the two parties are given by the following table, where
VH > P > VL and p > CH > CL.
B
N
H
L
UHP, P- CH VLP, PCL
0,0
0,0
a) Solve for the Nash equilibria of the above stage game.
b) Suppose that the firm discounts payoffs at rate 6, where 0 < d < 1.
Each consumer at date t observes the actions of the firm and of previous
consumers in all previous periods, 1,2..., t - 1. Show that there exists a sub-
game perfect equilibrium where the firm provides high quality, if & is large
enough. (Hint: construct a trigger strategy equilibrium).
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