代做Question 1调试R语言程序

1 Question 1

(15 points) Suppose there are I firms in an industry. Each firm can try to convince Congress to implement a subsidy in this industry. Let hi ≥ 0 denote the hours of effort put in by firm i. When the effort levels of the firms are h = (h1, h2,...,hI ), the value of the subsidy that gets approved is:

where a, b ≥ 0 are constants. The cost of effort to firm i is c(hi) = wh2i where w > 0 is a constant. Firm i’s payoff is si − c(hi).

(a) (10 points) For what set of parameters a, b, w do the firms have a dominant strategy?

(b) (5 points) Make a prediction about the size of the subsidy when your conditions in (i) are satisfied.

2 Question 2

(15 points) Consider a two-player game in which player 1 chooses a number (n1) on the interval [0, 1) and player 2 chooses a number (n2) on the interval (−1, 0] and the payo↵s to each player are II = n1n2

(a) (3 points) (i) Find strictly dominated strategies for each player, if any. (ii) Does IESDS yield a unique solution to this game?

(b) (12 points) Now, consider weakly dominated strategies. (i) Find weakly dominated strategies for each player, if any. (ii) Does IEWDS yield a unique solution to this game? If so, does the order of deletion matter?

3 Question 3

(10 points) Assume x ≥ 0. Find all pure strategy NE of the following game. Can you make a prediction about the outcome of the game?

4 Question 4

(20 points) The price in the market is given by P(q1, q2)=1− q1 − q2, where q1 and q2 are the quantities produced by the two firms. The cost function of each firm is given by:

(a) (10 points) Suppose α = β = 1. Find the Nash equilibrium output levels when the firms choose outputs simultaneously.

(b) (10 points) Suppose β = 1 is held fixed. What do you expect to happen to equilibrium quantities when (i) α increases from 1 (ii) α decreases from 1? Draw best responses to support your claim. (No need to solve for actual quantities)