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Homework Assignment 1
ECON6025 Strategic Behaviour
INSTRUCTIONS
1. There are two parts. Part A consists of MCQ that are a little different to what you may be accustomed to. There is not necessarily a unique correct choice - multiple options may be correct. For questions with multiple correct answers, total points for a question are divided equally between each correct selection. I deduct points if you are over-selecting answers. For example: To illustrate, suppose (a) and (b) are the only two correct answers to a 10 point question.
your choice mark Explanation |
||
a,b |
10 |
Full mark |
a,b,c |
5 |
(5 deducted for choosing (c), since ) |
|
|
you choose three options when only two are correct |
a,d |
5 |
no deduction for choosing the incorrect (d), |
|
|
since only two options are chosen |
2. Part B has one question for which you will have to upload a handwritten answers as a PDF file.
3. Each of the TEN questions in Part A is worth 10 points. The only question in Part B is worth 20 points.
4. This Assignment is worth 10% of your final grade
Part A
Question 1. In a strategic form game,
a) players make their choices simultaneously.
b) players jointly choose their strategies.
c) one player can always guess what other players are going to play.
d) None of the above.
Question 2. The game below shows the payoffs of only player 1. Restrict attention only to pure strategies.
a) Player 1 has a weakly dominant strategy.
b) Player 1 has a strongly dominant strategy.
c) Player 1 has a weakly dominated strategy.
d) None of the above.
Question 3. Reconsider the game in Question 2. Now allow for mixed strategies.
a) Player 1 has a weakly dominant strategy.
b) Player 1 has a strongly dominant strategy.
c) Player 1 has a strongly dominated strategy.
d) None of the above.
Question 4. In the following game,
a) (A,L) could be an IEDS solution.
b) (A,C) is the unique rationalizable strategy.
c) (B,C) is an IEDS solution.
d) None of the above.
Question 5. In a Nash equilibrium of a game,
a) Each player receives the highest of all the possible payoffs in the game.
b) Each player receives the highest payoff among all strategies, while fixing the strategy of her opponent(s).
c) payoffs may be such that both players can gain by jointly choosing some other strategy combination.
d) Both (b) and (c).
Question 6. In a two player strategic form game, if s* is a weakly dominant strategy for one of the players, then
a) s* must be played in every pure strategy Nash equilibrium of this game.
b) the game is necessarily dominance solvable.
c) s* is the unique rationalizable strategy.
d) None of the above.
Question 7. Consider a two player game in which (s1 ;t1) and (s2 ;t2) are two Nash equilibria such that s1 ≠ s2 and t1≠t2.
a) Such a game may be dominance solvable.
b) Such a game has more than one rationalizable strategy profile.
c) Both (a) and (b).
d) Neither (a) nor (b).
Question 8. It is known that in a certain market with two firms, setting a price of p2(*)=2 is a weakly dominant strategy for Firm 2. Suppose that the profits of Firm 1 are given by u1 (p1 ;p2)=(12¡p1 ¡p2)p1 for arbitrary values of p1 and p2. Firm 1 is allowed to choose any non-negative price.
a) (p1(*);p2(*))=(5;2) must be a Nash equilibrium of this game.
b) (p1(*);p2(*))=(5;2) is the only Nash equilibrium of this game.
c) Firm 2 must set a price of 2 in every Nash equilibrium of this game.
d) There is not enough information to conclude any of the above.
Question 9. The following figure shows the reaction functions of two players involved in a game with two strategies each. (The thick line is the reaction function of P2 and the wiggly line is that of P1). The horizontal axis depicts the probability of player 1 choosing strategy 1 and the vertical axis shows the probability of player 2 choosing her first strategy. This game
a) has a unique Nash equilibrium.
b) has no pure strategy equilibria.
c) has only pure strategy equilibria.
d) has both both pure and mixed strategy equilibria.
Question 10. The following figure shows the reaction functions of two players involved in a game with two strategies each. (The thick line is the reaction function of P2 and the wiggly line is that of P1). The horizontal axis depicts the probability of player 1 choosing its first strategy and the vertical axis shows the probability of player 2 choosing her first strategy. This game
a) has a unique Nash equilibrium.
b) P1 has a weakly dominant strategy.
c) P1 has a strongly dominant strategy.
d) None of the above.