For the following game, if the saddle point exists, find the strategies producin
ID: 3143221 • Letter: F
Question
For the following game, if the saddle point exists, find the strategies producing the saddle point, and the value of the game. Also, decide if the game is strictly determined. left bracket Start 3 By 2 Matrix 1st Row 1st Column negative 11 2nd Column negative 15 2nd Row 1st Column negative 19 2nd Column negative 10 3rd Row 1st Column negative 4 2nd Column negative 6 EndMatrix right bracket 11 15 19 10 4 6 Does a saddle point exist? No Yes What is the saddle point?nothing What are the strategies producing the saddle point?nothing (Type an ordered pair.) What is the value of the game?nothing Is the game strictly determined? Yes No
Explanation / Answer
Solution
The pay-off matrix is presented below in a tabular form along with row min and column max
Row No
Column No.
Row min
1
2
1
- 11
- 15
- 15
2
- 19
- 10
- 19
3
- 4
- 6
- 6
Column max
- 4
- 6
-
A game has a saddle point if there is an element in the pay-off matrix that is both lowest element in its rows (i.e., row min) and highest element in its columns (i.e., column max).
From the table we see that – 6 satisfies this criterion.
Hence, this game has saddle point. ANSWER 1
The saddle point is – 6 ANSWER 2
Strategy producing saddle point is (3, 2) ANSWER 3
Value of the game is – 6 ANSWER 4
Row No
Column No.
Row min
1
2
1
- 11
- 15
- 15
2
- 19
- 10
- 19
3
- 4
- 6
- 6
Column max
- 4
- 6
-