*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?

(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

**4 **In the following game, in which *s*1 = (*p, *1 *− **p*) is Player 1’s strategy and *s*2 = (*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 *s*1 = (*p, *1 *− **p*) is Player 1’s strategy and *s*2 = (*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

**7 **The following game:

(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:

**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 *s*1 = (*p**T **, p**M**, p**B*) be the strategy of Player 1 (with *p**i *the probability of action *i*) and *s*2 = (*q**L**, q**C**, q**R*) be the strategy of Player 2 (with *q**i *the probability of action *i*). Which is false for the following game?

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

(B) *s*1 = (0*.*5*, *0*.*5*, *0) and *s*2 = (0*.*5*, *0*.*5*, *0) is a Nash equilibrium

(C) *s*1 = (0*.*25*, *0*.*75*, *0) and *s*2 = (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 *t**i **∈ *[0*, **∞*) and the utility function of player *i *is

where *i ≠**j *and *v*1 = 20*, v*2 = 10. Which of the following is not a pure strategy Nash equilibrium of this game?

**14 **Consider a Cournot duopoly. The market demand function is *P *= 130 *− *(*q*1 + *q*2), where *P *is the market price, *q*1 is the output produced by Firm 1 and *q*2 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 *− *(*q*1 + *q*2), where *P *is the market price, *q*1 is the output produced by Firm 1 and *q*2 is the output produced by Firm

- Firms 1 have a constant marginal cost of
*c*1 = 10, while Firm 2 has a constant marginal cost of*c*2 = 40. Which is false?