# Self Test Questions

#### Theory

1. What is 'two-person zero-sum game' ?

2. Define the following:

• Pure strategy.
• Pay-off matrix.
• Optimal strategies

3. Explain briefly the importance of the principle of dominance.

4. What are the advantages & limitations of game theory?

### Practical

1. Consider the game whose pay-off matrix is given below. Find its solution.

On small screens, use horizontal scrollbar to view full table

Player B
Player A   I II III
I -4 -6 3
II -3 -3 6
III 2 -3 4

2. Two companies A and B are competing for the same product. Their different strategies are given in the following pay-off matrix:

Company B
Company A   I II III
I 2 -2 3
II -3 5 -1

Determine the best strategies and find the value of the game.

3. Solve the following games:

(a)
Player B
Player A   I II III IV V
I 4 0 1 7 -1
II 0 -3 -5 -7 5
III 3 2 3 4 3
IV -6 1 -1 0 5
V 0 0 6 0 0

(b
Player B
Player A   I II III
I -2 15 -2
II -5 -6 -4
III -5 20 -8

(c)
Player B
Player A   I II III
I 2 -1 3
II 2 -1 2
III -1 0 0
IV 2 0 4

(d)

On small screens, use horizontal scrollbar to view full table

Player B
Player A   I II III IV
I -5 3 1 20
II 5 5 4 6
III -4 -2 0 -5

(e)
Player B
Player A   I II III IV
I 3 -5 0 6
II -4 -2 1 2
III 5 4 2 3

4. Use the dominance principle to solve the following game:

 0 0 0 0 0 0 4 2 0 2 1 1 4 3 1 3 2 2 4 3 7 -5 1 2 4 3 4 -1 2 2 4 3 3 -2 2 2

5. Solve the following games:

(a)

Player B
Player A   I II III
I -5 -1 -1
II 4 0 2
III -5 2 0

(b)
Player B
Player A 6 8 3 13
4 1 5 3
8 10 4 12
3 6 7 12

6. Solve the following game algebraically

Player B
Player A   I II III
I 4 2 4
II 2 4 0
III 4 0 8

7. Reduce each of the following games by using the rule of dominance and then solve the reduced game by any of the method you have studied:

(a)
B1 B2 B3
A1 3 8 5
A2 6 2 7
A3 4 5 6

(b)
B1 B2 B3 B4 B5
A1 8 7 6 -1 2
A2 12 10 12 0 4
A3 14 6 8 14 16

8. Two players A & B, without showing each other put a coin on a table with head or tail up. If the coins show the same side (both head or tail), the player A takes both the coins, otherwise B gets them. Construct the matrix of the game and solve it.

9. In a game of matching coins with two players, suppose A wins one unit of the value when there are two heads; wins nothing when there are two tails and loses 1/2 units of value when there is one head and one tail. Determine the pay off matrix, the optimal strategies for both the players.

Share and Recommend