代做EC202 Microeconomics 2 March Examinations 2022/23代做留学生SQL语言程序

日期：2024-08-27 04:13

EC202 – Course test

Microeconomics 2

March Examinations 2022/23

1. Consider the following two-player simultaneous-move game:

Which statement is true? (6 marks)

A. There is one unique pure-strategy Nash equilibrium (U, L).

B. There are two pure-strategy Nash equilibria of the game – (U, L) and (D, R) – and one mixed-strategy Nash equilibrium.

C. There are infinitely many Nash equilibria of this game.

D. All outcomes of the game are Pareto efficient.

E. There are exactly two Nash equilibria of the game.

2. Consider the following three-player simultaneous-move game:

(6 marks)

A. There are exactly two Nash equilibria of the game.

B. There are exactly three Nash equilibria of the game.

C. There are infinitely many Nash equilibria of the game.

D. There is a mixed-strategy Nash equilibrium of the game in which Player 1 plays U or D with equal probability; Player 2 plays L or R with equal probability and Player 3 plays B with probability 1.

E. Action R is a strictly dominant strategy.

3. Ram is faced with a lottery which pays £100 in a good state and £k in a bad state with each state occurring with equal probability and k < 100. Ram’s utility function is u(x) = √x. For which value of k is Ram indifferent between taking the lottery and receiving £81 for certain.   (6 marks)

A. We have insufficient information to answer this question.

B. k = £54.

C. k = £64.

D. k = £44.

E. k = £74.

4. Consider Xiaoming whose preferences can be represented by the following utility function:

u(x) = ln(x + 1),

where x is wealth. Which statement is true? (6 marks)

A. Xiaoming’s coefficient of absolute risk aversion is decreasing in wealth, and his coefficient of relative risk aversion is increasing in wealth.

B. Xiaoming’s coefficient of absolute risk aversion is constant, and his coefficient of relative risk aversion is increasing in wealth.

C. Xiaoming is risk neutral.

D. Xiaoming would choose a lottery that would pay £100 or £0 with equal probability over receiving £25 for certain.

E. Xiaoming would choose a lottery that would pay £100 or £0 with equal probability over receiving £20 for certain.

5. Consider a simultaneous-move game with two players, L = {1, 2}, with actions S1 = S2 = {Rock, Paper, Scissors, Fire, Water}. The Rock (R) beats Scissors (S) and Water (W) and is beaten by Paper (P) and Fire (F); P beats R and W and is beaten by S and F; S beats P and W and is beaten by R and F; F beats R, P and S and is beaten by W; W beats F and is beaten by R, P and S. Every action draws with itself. A win gives a player a payoff equal to 1, lose gives -1, and a tie gives a payoff equal to 0. The normal-form. representation of the game takes the following form.

Which of the following statements is true? (6 marks)

A. There is a Nash equilibrium in which each player mixes between all actions with equal probability.

B. There is no Nash equilibrium of this game.

C. Action W cannot be played in any Nash equilibrium.

D. There is a Nash equilibrium in which each player mixes between R, P, S and F with equal probability, and where W is played with zero probability.

E. There is a Nash equilibrium in which each player play R, P and S, respectively, with probability 9/1 and in which they play F and W, respectively, with probability 3/1.

6. Consider a private-value auction in which two bidders, i = 1, 2, participate. Suppose the bidders valuations of the object being auctioned (vL and vH) take values 100 and 200, respectively, with equal probability (these are i.i.d realisations of a random variable). Suppose the seller has chosen a first-price sealed-bid auction for the object. The bidders can select any bid, bi ∈ R+. Which statement is true? (6 marks)

A. There is a pure-strategy Bayes-Nash equilibrium in which each type of bidder selects truthful bids – (vL → 100, vH → 200).

B. There is a pure-strategy Bayes-Nash equilibrium in which the low valuation type bids 100, and the high valuation type bids 150 – (vL → 100, vH → 150).

C. The Bayes-Nash equilibrium is Pareto efficient.

D. The low valuation type has no weakly dominant strategy.

E. There is no Bayes-Nash equilibrium.

7. Consider the following two-player simultaneous-move game:

Each player discounts the future by δ ∈ [0, 1]. If the game is repeated over time, we assume deviation from a cooperative outcome is followed by defection forever or until the game ends. Which statement is true? (6 marks)

A. If the game is repeated for a finite number of periods, the outcome (M, M) can be sustained in all but the last period.

B. The stage game has no mixed-strategy Nash equilibrium.

C. In the infinitely-repeated game, cooperation on (M, M) can be sustained if and only if δ > 4/1.

D. In the infinitely-repeated game, cooperation on the outcome (M, M) can be sustained for δ > 2/1.

E. There is no pure-strategy Nash equilibrium in the stage game.

8. Consider the following two-player simultaneous-move game:

Which of the following statements is true? (6 marks)

A. The game has infinitely many Nash equilibria.

B. There are only two Nash equilibria of the game.

C. There are exactly two Pareto efficient outcomes of the game.

D. There is a mixed-strategy Nash equilibrium in which Player 2 plays R with probability ρ2 = 1 and Player 1 plays U with probability ρ1 = 10/1.

E. There are exactly three Nash equilibria of the game.

9. Consider the following two-player simultaneous-move game:

where k > 0. Which statement is true? (8 marks)

A. There is at most two pure-strategy Nash equilibria of the game.

B. There are infinitely many Nash equilibria of the game.

C. Outcomes (U, L) and (D, R) are Pareto efficient if and only if k > 7.

D. Action L weakly dominates R.

E. There is a mixed-strategy Nash equilibrium of the game.

10. Consider the following two-player simultaneous-move game:

Which statement is true? (6 marks)

A. There is exactly one mixed-strategy Nash equilibrium of the game.

B. The number of Pareto efficient outcomes of the game does not exceed five.

C. Action M weakly dominates action R.

D. There are exactly five pure-strategy Nash equilibria of the game.

E. Action X is strictly dominated.

11. Consider the following “war of attrition” game, which is played over discrete periods of time. Player 1 and Player 2 can play Stop (S) or Continue (C). We can represent the game in normal form. as follows:

The length of the game depends on the players’ behaviour. Specifically, if one or both players select S in a period, then the game ends at the end of this period. Otherwise, the game continues into the next period. Suppose the players discount payoffs between periods according to the discount factor δ ∈ (0, 1). Which statement is true? (8 marks)

A. There are infinitely many subgames of the game.

B. There is no pure-strategy Nash equilibrium of the game.

C. The expected payoff to each player in the mixed-strategy Nash equilibrium is strictly negative.

D. No equilibrium action is consistent with play that proceeds beyond the first period.

E. Action S strictly dominates action C.

12. Consider Paula who is facing the following gamble. With probability ρ = 5/1 she will end up in a “bad state” and consume xb =£3 and with probability 1 − ρ = 5/4 she will consume xg =£100 in a “good state”. Paula’s utility can be represented as u(xi) = ln xi, where i = b, g. Suppose there is an insurance contract available to the individual offering K units of insurance for a premium of 5/2K. How much insurance will Paula buy? (6 marks)

A. K = 36

B. K = 46

C. K = 56

D. K = 66

E. K = 76

13. Consider the following simultaneous-move three-player game:

Which statement is true? (8 marks)

A. There are three pure-strategy Nash equilibria of the game.

B. There is no Nash equilibrium of the game.

C. There is a finite number of Nash equilibria of the game.

D. There are exactly three Nash equilibria of the game.

E. There is one unique Nash equilibrium of the game – {(D, L, A)}.

14. Consider the following dynamic game of incomplete information:

There are two players in the game – Player E and Player P. The timing of the game is as follows. Nature draws a type ti , from the set of types, T = {t1, t2}. Each type, t1 and t2 are drawn with equal probability. Player E observes their type, ti , and chooses a message mi from a set of messages, M = {m1, m2}. Player P observes mi (but not ti) and then chooses an action ak from a set of feasible actions, A = {a1, a2}. The payoffs from each action are illustrated in the extensive form. representation of the game above as pairs (x, y) with the first entry denoting the payoff to Player E and the second the payoff to Player P. For which values of k is there a separating equilibrium in which a type t1 Player E selects m2 and in which a type t2 Player E selects m1? (8 marks)

A. No values of k.

B. All values of k.

C. k ≥ 1.

D. k ≥ 0.

E. k ≥ -1.

15. Consider the following prisoner’s dilemma:

where C is cooperate and D is defect. Suppose the two players adopt a cooperative strategy which involves alternating between actions D and C. In period t, Player 1 plays C and Player 2 plays D; in period t + 1, Player 1 plays D and Player 2 plays C. Assume that Player 1 and Player 2 discount the future by δ = 2/1. We also assume that any deviation from the alternating equilibrium is followed by infinite defection (grim-trigger). For which values of k can the players sustain the cooperative outcome? (8 marks)

A. k ≤ 8.

B. k ≤ 7.

C. k ≤ 6.

D. k ≤ 5.

E. k ≤ 4.