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ECON2000 5 Quiz5 - after-class quiz 5
Competition And Strategy (ECON20005)
University of Melbourne
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ECON20005 Competition and Strategy: Quiz 5
Question 1
(Multiple Choice) Which of the following is not one of the features of a Prisoners’ Dilemma? a) The game must have at least two strategies for all players b) The Nash equilibrium outcome to the game is worse for all players than some other outcome in the game c) Any non-equilibrium outcome is better for all players d) The game requires at least two players
Question 2
(Multiple Choice) Which is the following is true of a two-player Prisoners’ Dilemma? a) Both players have strictly dominant strategies b) A Nash equilibrium can be solved for using iterated elimination of dominated strategies c) The game has a mixed strategy Nash equilibrium where both players choose probability distributions that only involve probabilities of 0 or 1 d) All of the above
Information for the remainder of the quiz
All subsequent questions in this quiz are based on the following game, represented in normal form:
Player 2 a b Player 1 a 3,3 8, b 2,9 7,
Question 3
(True/False) If this game is played twice, a unique SPNE is created where both players will always play a whenever they have the opportunity to move. a) True b) False
Question 4
(True/False) If this game is played 10,0 00 times, then it is possible for an SPNE to exist where both players co-operate by playing b as long as the other player is also playing b. a) True b) False
Question 5
(Multiple Choice) Suppose that both players are attempting to co-operate on the outcome ( b,b ). What would the players receive in the event of unilateral deviation from this outcome? a) Player 1 receives 9 and player 2 receives 8 b) Player 1 receives 8 and player 2 receives 9 c) Both players receive 8 d) Both players receive 9
Question 6
(Multiple Choice) Suppose that this game is infinitely repeated and that both players discount future payoffs by some discount factor 0 < 𝛿 < 1. If both players adopt the grim strategy, for what values of 𝛿 would player 1 be willing to co-operate on the outcome ( b,b ) forever? a) Discount factor greater than 1/ b) Discount factor greater than 1/ c) Discount factor below 1/ d) Discount factor below 1/
Question 7
(Multiple Choice) Suppose that this game is infinitely repeated and that both players discount future payoffs by some discount factor 0 < 𝛿 < 1. If both players adopt the grim strategy, for what values of 𝛿 would player 2 be willing to co-operate on the outcome ( b,b ) forever? a) Discount factor greater than 1/ b) Discount factor greater than 1/ c) Discount factor below 1/ d) Discount factor below 1/
Question 8
(Multiple Choice) Suppose that this game is infinitely repeated and that the players attempt to co- operate on ( b,b ) adopting the grim strategy for all players. If both players have a common discount factor of 0, then in equilibrium, we would observe that a) Player 1 will play b every period while player 2 plays a b) Player 1 will play a every period while player 2 plays b c) Both players play a every period d) Both players play b every period
Question 9
(Multiple Choice) What piece of information, if known, would guarantee that co-operation on ( b,b ) every period is sustainable in equilibrium? a) Both players have a discount factor above 1/ b) Both players have a discount factor above 1/ c) Both players have discount factors below 1/ d) Both players have a discount factor above zero
Quiz Solutions
Question Solution 1 c 2 d 3 a 4 b 5 b 6 b 7 a 8 c 9 a 10 b
ECON2000 5 Quiz5 - after-class quiz 5
Course: Competition And Strategy (ECON20005)
University: University of Melbourne
