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ECON 437: Game Theory

Practice Midterm 2

For the first 10 questions in this exam, consider the following Extended Form Game:

1.    According to backwards-induction, in how many moves does the game end?

2.    According to backwards-induction, what is the outcome of the game?

3.    What is the set of strategies for player 1?

4.    What is the set of strategies for player 2?

5.    What is the set of NashEquilibria?

6.    What is the Subgame Perfect Nash Equilibrium?

7.    Player 2 threatens that she will play R no matter what. Is this threat credible? True or false.

8.    What is the pay-off that player 2 derives from the strategy profile ((R,R),(L,R))?

9.    What is the pay-off that player 1 derives from the strategy profile ((R ,L),(R,R))?

10.  What is the best response for player 2 if player 1 plays (R,R)?

For questions 11-16, consider the following duopoly:

.     Both firms produce a homogenous product. Each firm has the following cost structure: TC(q% ) = 2q%   + 2

.     Firm 1 chooses the quantity it will supply first.

.     Firm 2 chooses how much it will supply after observing the quantity supplied by firm 1.

.     The market clears after both firms have chosen their quantities supplied. The demand in this market is Q+   = 20 − P

11.  What is the outcome of this game?

12.  What is the Subgame Perfect Nash Equilibrium?

13.  What is the price in equilibrium?

14.  What are the profits of firm 1 in equilibrium?

15.  True or false. Is the strategy profile  a Nash Equilibrium?

16.  In the strategy (9,4.5) , who is playing a non-credible threat?

For questions 17-20, consider the following duopoly:

.     Firms produce a differentiated product. Each firm has the following cost structure: TC(q% ) = 2q%   + 2 .

.     The demand for product i is q%  = 10 − p%   + p< .

.     Firm 1 chooses the price it will sell its product at first.

.     Firm 2 chooses its price after observing the price of firm 1.

17.  What is the outcome of this game?

18.  What is the Subgame perfect Nash Equilibrium?

19.  What are the profits of firm 1 in equilibrium?

20.  Who supplies more? Firm 1 or Firm 2?