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P1 \ P2 Left Middle Right Left 4,2 3,3 2,1 Middle 3,3 5,5 6,2 Consider the simultaneous move game represented by this payoff matrix. Suppose that the game is repeated for two periods and the players know that the game will end at the end of two periods. They observe the first period outcome before they move to the second period. Assume that there is no discounting, i.e. 2nd period payoffs are not discounted, or the discount factor is equal to 1. Which of the following outcomes could occur in some subgame perfect equilibrium (SPE) of this two period repeated game? Choose True if you think the outcome can be a SPE, otherwise choose False. a) (Left, Left) is played in both periods. b) (Right, Right) is played in both periods. c) (Middle, Middle) is played in both periods. d) (Middle, Middle) is played Right 1,2 2,6 3,3 ◆ ◆ first period, followed by (Left, Left). ◆ e) (Middle, Middle) is played in the first period, followed by (Right, Right). Now suppose that the game is infinitely repeated. Denote the discount factor of the players as d. What is the threshold d* such that when

P1 \ P2 Left Middle Right Left 4,2 3,3 2,1 Middle 3,3 5,5 6,2 Consider the simultaneous move game represented by this payoff matrix. Suppose that the game is repeated for two periods and the players know that the game will end at the end of two periods. They observe the first period outcome before they move to the second period. Assume that there is no discounting, i.e. 2nd period payoffs are not discounted, or the discount factor is equal to 1. Which of the following outcomes could occur in some subgame perfect equilibrium (SPE) of this two period repeated game? Choose True if you think the outcome can be a SPE, otherwise choose False. a) (Left, Left) is played in both periods. b) (Right, Right) is played in both periods. c) (Middle, Middle) is played in both periods. d) (Middle, Middle) is played Right 1,2 2,6 3,3 ◆ ◆ first period, followed by (Left, Left). ◆ e) (Middle, Middle) is played in the first period, followed by (Right, Right). Now suppose that the game is infinitely repeated. Denote the discount factor of the players as d. What is the threshold d* such that when

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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P1 \ P2 Left Middle Right Left 4,2 3,3 2,1 Middle 3,3 5,5 6,2 Consider the simultaneous move game represented by this payoff matrix. Suppose that the game is repeated for two periods and the players know that the game will end at the end of two periods. They observe the first period outcome before they move to the second period. Assume that there is no discounting, i.e. 2nd period payoffs are not discounted, or the discount factor is equal to 1. Which of the following outcomes could occur in some subgame perfect equilibrium (SPE) of this two period repeated game? Choose True if you think the outcome can be a SPE, otherwise choose False. a) (Left, Left) is played in both periods. b) (Right, Right) is played in both periods. c) (Middle, Middle) is played in both periods. d) (Middle, Middle) is played 01/2 01/3 01/4 02/5 Right 1,2 2,6 3,3 ◆ ◆ first period, followed by (Left, Left). ◆ e) (Middle, Middle) is played in the first period, followed by (Right, Right). Now suppose that the game is infinitely repeated. Denote the discount factor of the players as d. What is the threshold d* such that when dzd* (Middle, Middle) is sustainable as a subgame perfect equilibrium by grim trigger strategies, but when d<d* playing Middle in all periods is not a best response? [HINT: Here the grim strategy is: "Play Middle in the first period. In the subsequent periods, play Middle if the outcome in all previous periods was (Middle, Middle)--i.e. both players chose Middle; otherwise, play Right."]
Transcribed Image Text:P1 \ P2 Left Middle Right Left 4,2 3,3 2,1 Middle 3,3 5,5 6,2 Consider the simultaneous move game represented by this payoff matrix. Suppose that the game is repeated for two periods and the players know that the game will end at the end of two periods. They observe the first period outcome before they move to the second period. Assume that there is no discounting, i.e. 2nd period payoffs are not discounted, or the discount factor is equal to 1. Which of the following outcomes could occur in some subgame perfect equilibrium (SPE) of this two period repeated game? Choose True if you think the outcome can be a SPE, otherwise choose False. a) (Left, Left) is played in both periods. b) (Right, Right) is played in both periods. c) (Middle, Middle) is played in both periods. d) (Middle, Middle) is played 01/2 01/3 01/4 02/5 Right 1,2 2,6 3,3 ◆ ◆ first period, followed by (Left, Left). ◆ e) (Middle, Middle) is played in the first period, followed by (Right, Right). Now suppose that the game is infinitely repeated. Denote the discount factor of the players as d. What is the threshold d* such that when dzd* (Middle, Middle) is sustainable as a subgame perfect equilibrium by grim trigger strategies, but when d<d* playing Middle in all periods is not a best response? [HINT: Here the grim strategy is: "Play Middle in the first period. In the subsequent periods, play Middle if the outcome in all previous periods was (Middle, Middle)--i.e. both players chose Middle; otherwise, play Right."]
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