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高等微观经济学代写 Economics 3382A-001代写 经济学代考

170

Midterm Exam

110 minutes

PLEASE NOTE THAT ANSWERS WITHOUT EXPLANATION WILL NOT BE GIVEN FULL CREDIT

Problem 1 (20 points) 高等微观经济学代写

You need to decide whether to buy the good today or wait until tomorrow. The good is worth \$100 to you. The price today is \$40, so if you buy it today, then your payo§ is \$60. If you wait, then with probability 0.4 somebody else will buy it today, and your payoff will be \$0. If you wait, and the good is not sold to anyone today, then tomorrow the price will go down to \$20, and so your payoff from buying discounted good will be \$80.

(a) (5 points) Draw a decision tree for this problem.

(b) (5 points) What is your best choice of action and its expected payoff?

Now suppose a “buying advisor” offers to tell you whether the good will be sold to someone else if you decide to wait or not sold. After you hear the advice you will choose whether to buy today or wait until tomorrow. The buying advisor is completely trustworthy and can perfectly foresee the future.

(c) (10 points) What is the value of perfect information provided by the buying advisor?

Problem 2 (25 points) 高等微观经济学代写

Consider the following all-pay auction game. Player 1 values the good at \$5, player 2 values the good at \$1. Each player can bid either \$0, \$1, or \$2. If a player bids more than the opponent, then she wins the good. If both players bid the same amount, then a coin is tossed to determine who the winner is, and the winner gets the good.

Both players always pay their bids regardless whether they win or lose.

(a) (5 points) Write down the normal form of this game.

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

(c) (5 points) Is there a strictly dominant strategy equilibrium?

(d) (5 points) Solve the game by iterated elimination of strictly dominated strategies.

(e) (5 points) What are the pure strategy Nash equilibria of this game?

(a) (7 points) Find the pure strategy best response function of each firm.

(b) (8 points) Find all pure strategy Nash equilibria of this game.

Now suppose firm 2 in addition faces a technological constraint that allows it to choose only between two levels of production: q2 = 0 or 12. Everything else remains the same as before.

(c) (5 points) Find the pure strategy best response function of each firm.

(d) (5 points) Find all pure strategy Nash equilibria of this game.

Problem 4 (30 points). 高等微观经济学代写

Consider the following second-price auction game. Player 1 values the good at \$3, player 2 values the good at \$1. Each player can bid either \$0 or \$1. If a player bids more than the opponent, then she wins the good. If both players bid the same amount then a coin is tossed to determine who the winner is, and the winner gets the good. The winner pays the bid submitted by the other player; the other player pays nothing.

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

(b) (5 points) Which of the playersístrategies are rationalizable?

(c) (10 points) Find all pure and mixed strategy Nash equilibria of this game.

Now suppose both players value the good at \$0.5. Everything else remains the same.

(e) (10 points) Find all pure and mixed strategy Nash equilibria of this game.

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