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 asingle consumer who only lives for one period. The consumer must choosebetween the actions BUY and NOT BUY (i.e. B and N). The firm mustchooose what quality level to provide, i.e. it must choose between H andL. The payoffs to the two parties are given by the following table, whereVH > P > VL and p > CH > CL.BNHLUHP, P- CH VLP, PCL0,00,0a) 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 previousconsumers 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 largeenough. (Hint: construct a trigger strategy equilibrium).

A stage game is where the players move simultaneously, one stage payoff will not affect the other,…

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).

Economics: Private and Public Choice (MindTap Course List)

16th Edition

ISBN:9781305506725

Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson

Publisher:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson

Chapter24: Price-searcher Markets With High Entry Barriers

Section: Chapter Questions

Problem 12CQ

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