Suppose the stage game was played an infinite amount of times, and let x = 13: P2 C D E 5,5 0,13 0,0 13,0 3,3 0,0 0,0 0,0 1,1 C P1 D E Now consider the following strategy: • In the first round, play C In all future rounds: If both players played C in all previous rounds, play C. - Otherwise, play E. Let the discount factor for both players be 8 € (0,1). What is the lowest value of such that both players using this strategy can be a SPNE? (a) This strategy profile is a SPNE for any & € (0,1) 9 (b) 8 > 2/3 13 (c) 8> ²/ 1 (d) 8 > }/ 3 (e) This strategy profile cannot be a SPNE for any 8 € (0, 1)

Suppose the stage game was played an infinite amount of times, and let x = 13: P2 C D E 5,5 0,13 0,0 13,0 3,3 0,0 0,0 0,0 1,1 C P1 D E Now consider the following strategy: • In the first round, play C In all future rounds: If both players played C in all previous rounds, play C. - Otherwise, play E. Let the discount factor for both players be 8 € (0,1). What is the lowest value of such that both players using this strategy can be a SPNE? (a) This strategy profile is a SPNE for any & € (0,1) 9 (b) 8 > 2/3 13 (c) 8> ²/ 1 (d) 8 > }/ 3 (e) This strategy profile cannot be a SPNE for any 8 € (0, 1)

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.9P

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see image Use the following setting for questions 1-3. Consider the following static game: C R L 3,1 0,0 5,0 T M 2,1 1,2 3,1 B 1.2 0,1 4,4 Suppose this game is played for two periods. At the beginning of period 2, the players can observe the outcome from period 1. There is no discounting. 1. First, assume only pure-strategy SPNE such that either player's second period strategy DOES NOT depend on the first period outcome. How many such SPNE are in this game? (a) 1 (b) 2 (c) 3 (d) 4 (e) none 2. Consider only SPNE from the previous question. What is the maximum sum of the players' payoffs that can be achieved in the first period? (a) 0 (b) 3 (c) 4 (d) 5 (e) 8 3. Now consider all possible pure-strategy SPNE such that (B,R) is played in the first period. What must be the equilibrium outcome in the second period of such SPNE? (a) (T,L) (b) (M,C) (c) (B,R) (d) (T,R) (e) There are no such SPNE
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