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# 经济学考试助攻 Economics 3382A-001代写 经济学考试代写

177

## Practice Final Exam

Time: 120 minutes

Answers without explanations will not be given full credit

### Problem 1 (25 points) 经济学考试助攻

Each of 3 players chooses whether to contribute \$1 toward the provision of a public good. The good is provided if and only if at least one player contributes. Contributions are never refunded to the players regardless of how many players contributed. Each player receives benefit \$4 if the public good is provided, and \$0 if the public good is not provided. If a player contributes, then she pays the cost \$1; if she does not contribute, then she pays no cost.

(a) Find all rationalizable strategies for each player.

(b) Find all pure strategy Nash equilibria.

(c) Find the symmetric mixed strategy Nash equilibrium where each player is using the same mixed strategy: contribute with probability p, not contribute with probability 1 p (where 0 < p < 1).

(d) Compute the players’expected payoffs in all equilibria and compare these payoffs for different equilibria.

### Problem 2 (25 points). 经济学考试助攻

Consider a two-player two-period game where each period the players play the following simultaneous move stage game:

After the first period the players observe what was played in the first period. The payoff of each player is the sum of the payoffs from the two periods. Throughout the question restrict attention to pure strategies.

(a) Can you find a subgame-perfect equilibrium of the entire game such that players play (A, a) in the first period? If your answer is ‘yes’, then find all such equilibria. If your answer is ‘no’, then explain your answer.

(b) Can you find a subgame-perfect equilibrium of the entire game such that players play (B, a) in the first period, and play (B; a) in the second period if (B; a) was played in the first period? If your answer is ‘yes’, then find all such equilibria. If your answer is ‘no’, then explain your answer.

(c) Can you find a Nash equilibrium of the entire game that is not a subgame-perfect equilibrium? Explain your answer.

### Problem 4 (25 points).

Consider an oligopoly situation when there are two firms, the inverse demand function is given by

where A is equally likely to be 30 or 0. Firm 1 learns the value of A before choosing its output. Firm 2 is aware of this fact but cannot itself observe the value of A. Both firms have identical total cost functions, C (q) = 0 for every q ≥ 0. They choose their outputs simultaneously.

Find the (pure strategy) Nash equilibrium of this game. (Assume that the firm produces nothing if it cannot make strictly positive profits).

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