Game Theory: Self Assessment Questions

1. What is a dominant strategy?

Write an answer in the box below and press submit. Take care with your spelling.

2. A Nash Equilibrium occurs where a player maximises their payoff given what they anticipate their opponent is doing

True
 False
3. In the following diagram the payoffs to player 1 are on the left-handside of the parentheses and those to player 2 on the right.

3a. Does Player 1 have a dominant strategy?

Yes
 No
3b. Does Player 2 have a dominant strategy?
Yes
 No

3c. What is the Nash Equilibrium? Please put your entry into the text box below using the following example - (top, left)

4. Consider the following 3-person game in which player 1 chooses the row, player 2 chooses the column and player 3 the matrix that will be played. The first number in each cell is the payoff to player 1, the second number is the payoff to player 2, and the third number the payoff to player 3.


What is the Nash Equilibrium for this game?
Top, Left, Matrix A
 Top, Right, Matrix A
 Top, Left, Matrix B
 Bottom, Left, Matrix B

5. In the following normal form game what is the Nash Equilibrium?

Blue and Red each play C
 Blue plays C, Red plays D
 Blue plays D, Red plays C
 Blue and Red each play D

6. What is the Nash Equilibrium in the following game between Kuwait and Saudi Arabia? The payoffs are net profits to each from producing millions of barrels of oil per day. If 5 million barrels per day are produced then the profit margins are £16 per barrel. If 6 million barrels per day are produced then the profit margins are £12 per barrel and they are £8 per barrel if 7million barrels per day are supplied.

a) Saudi produces 4 million barrels per day, Kuwait produces 1 million barrels per day.
 b) Saudi produces 4 million barrels per day, Kuwait produces 2 million barrels per day.
 c) Saudi produces 5 million barrels per day, Kuwait produces 1 million barrels per day.
 d) Saudi produces 5 million barrels per day, Kuwait produces 2 million barrels per day.
7. Which of the following statements describes Axelrod's portrayal of Tit-for-Tat?
Nice
 Defensible
 Provocable
 Forgiving
 Sensible

8. The game set out below shows the final stage of a ten period game between two firms. Profits/losses (in £millions per year) are depicted in the payoff matrix.

According to the logic of backward induction what should be the equilibrium of the game?

a) Firm 1 chooses a high price, Firm 2 chooses a high price.
 b) Firm 1 chooses a high price, Firm 2 chooses a low price.
 c) Firm 1 chooses a low price, Firm 2 chooses a high price.
 d) Firm 1 chooses a low price, Firm 2 chooses a low price.
©Kevin Hinde 1999 - 2004