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高等微观经济学代考 经济学代考

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高等微观经济学代考

Advanced Microeconomics I

Practice Midterm Exam

高等微观经济学代考 Problem 1 (25 points).You need to decide whether to take an umbrella today or not. You know that the probability of rain is p = 0:5 according to

Time: 110 minutes

Answers without explanations will not be given full credit

 

Problem 1 (25 points).  高等微观经济学代考

You need to decide whether to take an umbrella today or not. You know that the probability of rain is p = 0:5 according to the weather forecast. Your payo§ depends on your action and on the weather as follows:

action \ weather Rain Sun
Umbrella 80 20
No umbrella 0 100

(a) Draw a decision tree for this problem.

(b) What is your best choice of action and its expected payoff ?

Now suppose a “weather advisor” offers to tell you whether it will be raining or not. After you hear the advice you will choose whether to take umbrella or not. The weather advisor is completely trustworthy and truly knows what the weather will be like.

(c) What is the value of perfect information provided by the weather advisor?

(d) Suppose the probability of rain is p 2 [0; 1]. Are there any values of p for which the value of information is zero?

 

Problem 2 (25 points).   高等微观经济学代考

Consider the following version of p-beauty contest. There are 2 players, each player can choose a number from {0, 1, 2}. Players whose choice is closest to 3/2 of the average split $1 between themselves.

(a) Write down the game in matrix form.

(b) Find pure strategy best response for each player.

(c) Is there a strictly dominant strategy equilibrium?

(d) Which of the playersístrategies are rationalizable?

Now suppose only numbers in {0; 1} are allowed.

(e) Is it possible to have a mixed strategy Nash equilibrium in this game such that player 1 chooses 0 with positive probability?

 

高等微观经济学代考
高等微观经济学代考

 

(a) Find the pure strategy best response function of firm 1.

Next, find the pure strategy best response of firm 2 using steps (b), (c) and (d).

(b) Suppose firm 2 decides to produce q2 > 0 and expects firm 1 to produce q1. Find optimal q2 as a function of q1 , and substitute it into the the profit of firm 2.

(c) Compare the profit of firm 2 found in (b) with the profit from not producing (q2 = 0).

For which values of q1 is it optimal for firm 2 to shut down?

(d) Write down the pure strategy best response of firm 2.

(e) Find all pure strategy Nash equilibria of this game where each firm produces positive output.

(f) Find all pure strategy Nash equilibria of this game where at least one firm produces nothing.

(g) Check whether q2 = 1 is strictly dominated for firm 2.

 

Problem 4 (20 points).   高等微观经济学代考

Suppose two players have $20 to split in the game Golden Balls: Split or Steal as in Problem 3 in Problem set 3. If both choose Split, then each receives $10. If one chooses Steal and the second Split, then the person who chooses Steal gets $20 and the other gets nothing. If both choose Steal, then both get nothing. Player 1 only cares about the amount she receives. Player 2 is altruistic as follows: her payoff equals the amount that she receives plus half of the amount the opponent receives.

(a) (5 points) Write down the game in matrix form.

(b) (2 points) Find all pure strategy Nash equilibria.

(c) (13 points) Find all mixed strategy Nash equilibria.

高等微观经济学代考
高等微观经济学代考

 

 

 

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