ECON7070

Practice Test 2

ECON Test代写 Test 2 will be a combination of questions like the ones in tutorials 4,5,6 and the following questions.

Test 2 will be a combination of questions like the ones in tutorials 4,5,6 and the following questions.

1 Which is true for the following two-player game: ECON Test代写

(A) T is a best response to L

(B) (M,C) is the only Nash equilibrium

(C) (M,R) is a Nash equilibrium

(D) There is a mixed strategy Nash equilibrium in which player 2 chooses both C and R with positive probability

2 Which is false for the following game?

ECON Test代写
ECON Test代写

(A) (M,C) and (B,C) are the only pure strategy Nash Equilibria

(B) There is a Nash equilibrium in which R is played with positive probability

(C) There is no Nash equilibrium in which L is played with positive probability

(D) There is no Nash equilibrium in which both players choose two of their actions with positive probability

3 Which is true for the following game?

(A) There is a mixed strategy Nash equilibrium in which Player 1 plays both M and B with positive probability and Player 2 plays both L and C with positive probability

(B) The best response of Player 2 to M is C

(C) (B,C) is the only Nash equilibrium

(D) (M,L) is a Nash equilibrium

ECON Test代写
ECON Test代写

In the following game, in which s1 = (p, 1 p) is Player 1’s strategy and s2 = (q, 1 q) is Player 2’s strategy, Player 1 is indifffferent between U and D when q is equal to: [Write you answer as a decimal number, e.g. 0.33]

5 In the following game, in which s1 = (p, 1 p) is Player 1’s strategy and s2 = (q, 1 q) is Player 2’s strategy, Player 2 is indifffferent between L and R when p is equal to: [Write you answer as a decimal number, e.g. 0.33]

6 Which is true for the following game? ECON Test代写

(A) (T,R) is a Nash equilibrium

(B) There is a Nash equilibrium in which Player 1 plays M and B with equal probability and Player 2 plays each action L, C and R with positive probability

(C) There is a Nash equilibrium in which Player 1 plays each action T, M and B with positive probability and Player 2 plays each action L, C and R with positive probability

(D) There is a Nash equilibrium in which Player 1 plays M and B with equal probability and Player 2 plays L and C with equal probability

The following game:

ECON Test代写
ECON Test代写

(A) Has a pure strategy Nash equilibrium

(B) Has a mixed strategy Nash equilibrium in which Player 1 plays T, M and B with equal probability and Player 2 plays L C and R with equal probability

(C) Has a mixed strategy equilibrium in which Player 2 only puts positive probability on L and R

(D) Has a mixed strategy Nash equilibrium in which Player 1 plays M and B with probability 0.5 each and Player 2 plays L and C with probability 0.5 each

8 If Player 2 chooses L and R with equal probability and Player 3 chooses A and B with equal probability, then Player 1 best response is: ECON Test代写

(A) T

(B) M

(C) D

(D) Both M and D

9 In the following game, if Player 2 chooses L and R with equal probability and Player 1 chooses M, then Player 3’s expected utility from choosing A is:

ECON Test代写
ECON Test代写

10 Which is false for the following three player game?

(A) (D,T,T) is a Nash equilibrium

(B) (T,D,D) is a Nash equilibrium

(C) (T,D,T) is a Nash equilibrium

(D) None of the players has a dominant strategy

11 Which is false for the following game? ECON Test代写

(A) It has no pure strategy Nash equilibrium

(B) There exists a Nash equilibrium in which player 1 plays B with zero probability

(C) There exists a Nash equilibrium in which player 1 plays C with zero probability

(D) There exists a Nash equilibrium in which player 1 plays A with zero probability

12 Let s1 = (pT , pM, pB) be the strategy of Player 1 (with pi the probability of action i) and s2 = (qL, qC, qR) be the strategy of Player 2 (with qi the probability of action i). Which is false for the following game?

ECON Test代写
ECON Test代写

(A) (M,L) and (T,C) are the only pure strategy Nash equilibria

(B) s1 = (0.5, 0.5, 0) and s2 = (0.5, 0.5, 0) is a Nash equilibrium

(C) s1 = (0.25, 0.75, 0) and s2 = (0.75, 0.25, 0) is a Nash equilibrium

(D) In any strictly mixed strategy equilibrium, Player 1 puts positive probability on T and M only, and Player 2 puts positive probability on L and C only

13 Consider a simultaneous move game played by two players, Player 1 and 2. Player i’s action set is ti [0, ) and the utility function of player i is

where i ≠j and v1 = 20, v2 = 10. Which of the following is not a pure strategy Nash equilibrium of this game?

ECON Test代写
ECON Test代写

14 Consider a Cournot duopoly. The market demand function is P = 130 (q1 + q2), where P is the market price, q1 is the output produced by Firm 1 and q2 is the output produced by Firm 2. The two fifirms have a constant marginal cost c = 10. The pure strategy Nash equilibrium of this game is:

15 Consider a Cournot duopoly. The market demand function is P = 130 (q1 + q2), where P is the market price, q1 is the output produced by Firm 1 and q2 is the output produced by Firm

  1. Firms 1 have a constant marginal cost of c1 = 10, while Firm 2 has a constant marginal cost of c2 = 40. Which is false?
ECON Test代写
ECON Test代写

 
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