Question

Solve the following game by graphical method.

\begin{bmatrix} -2&0 \\ 3&-1 \\ -3&2 \\ 5&-4 \end{bmatrix}

14 Feb 2018
Answer :
Word Count : 601
We are asked to solve the 4×2 game with payoff matrix: $$ A = \begin{bmatrix} -2 & 0 \\ 3 & -1 \\ -3 & 2 \\ 5 & -4 \end{bmatrix} $$ using the graphical method. --- Step 1: Let player A use mixed strategies. Let the probabilities for player A choosing rows $R_1, R_2, R_3, R_4$ be $x_1, x_2, x_3, x_4 \ge 0$, with $$ x_1 + x_2 + x_3 + x_4 = 1 $$ Let the probability for player B choosing columns $C_1, C_2$ be $y$ for $C_1$ and $1-y$ for $C_2$. --- Step 2: Express expected payoff for player A. If A plays row $i$, expected payoff against B’s mixed strategy $y$ is: $$ E(R_i) = \text{payoff in column 1} \cdot y + \text{payoff in column 2} \cdot (1-y) $$ So: * $R_1: E_1 = -2y + 0(1-y) = -2y$ * $R_2: E_2 = 3y + (-1)(1-y) = 3y -1 + y = 4y -1$ * $R_3: E_3 = -3y + 2(1-y) = -3y +2 -2y = -5y +2$ * $R_4: E_4 = 5y + (-4)(1-y) = 5y -4 +4y = 9y -4$ --- Step 3: Plot these lines vs $y$ and find upper envelope. We can find the intersection points of these lines to determine optimal mixed strategy for B (minimizing A’s payoff). Step 3a: Find intersections $E_i = E_j$ 1. $E_1 = E_2: -2y = 4y -1 \implies 6y = 1 \implies y = 1/6$
________ __________ ___ ___ _________ __________ ___ _________ ___ ____ _________ _____.
____ _______ _____ __________ _______.
___ _______ ____ _____ _________ _____ ______ _____ ______ _________ _____ ________.
______ __________ ________ ______ ___ _____ ______ _________.
___ _______ ___ _____ ___.
_________ ___ ________ _____ _________ ______ ____ _____ __________.
___ ______ ________ ___ ______ ___.
_______ ________ ___ _____ _________ ____ _____ ____ ___ _____ _____ __________.
___ _________ _____ __________ _____ __________.
___ ________ _____ ______ _______ ____.
__________ ____ _________ __________ ______ _____ _______.
___ ____ ___ ____ _______ _____ __________ ___ _________ _______.
_______ _____ _____ ______ _________ _______ __________ __________ ___ ______ ____.
__________ ____ _____ ________ __________ ___ ___ ___ ______.
_________ ___ ____ __________ ________.
____ _____ _____ ____ ___ ________ _________ __________ _______ ____ ____.
______ _____ _____ ____ __________ _________.
______ _____ __________ _____ ___ __________.
____ ________ ___ _______ __________ ____ ________ _______ _____.
________ _____ __________ _________ ___ __________ __________ ___ ____ _______.
___ _____ _________ ___ ____ _____ _________ _________ ________.
________ _____ __________ ________ ______ _____ _______ _________ ___ _____.
__________ ________ _______ ______ __________.
______ ___ ___ ____ ____ _____ ________ __________.
_________ __________ __________ __________ _______ ____ ___ ___ ________ ______.
___ __________ __________ __________ __________ _________.
__________ ________ _________ __________ ____ _____ ___ ______.
____ __________ _________ ___ _________ _______ _________.
________ _____ _____ ___ _______ ________ _____ ___ _______ ______ ________.
___ _______ ___ ________ _______ _______ _____.
_____ ______ ________ ___ ____ ______ ____ _____ _______.
________ ____ _______ _____ _______ _________ ___ _________.
_______ _____ ______ _________ ______ _________ _____ ______ ______ _____ __________.
___ ________ ________ ____ ___ _____ ___.
___ _____ ____ _________ ________ _____ ____ ______ ___.
______ _______ _______ _________ ______ ____ ________ _____ _________ ______ ___ ___.
__________ ____ _________ ________ _________.
________ __________ ___ ____ ___ __________.
_________ ________ _____ _______ ____ _____ ___.
______ _____ ___ ________ ______ _________ _____ _____ _____ ___ ____.
___ ______ ______ __________ ___ _________ ________ _________ ________ __________ ______.
_____ ________ _________ _______ _________ ______ _________ ___ ____ _______ ____.
____ _________ ______ ___ ________ ____ ___ ________.
IGNOU ACADEMY
Your IGNOU journey, made easier.
  • Solved Assignments
  • Study Notes
  • Guess Papers
  • Question Papers
Call Us WhatsApp
STUDY • PREPARE • SUCCEED
Skip in 10
Related Questions

Solve the following game by graphical method.

\begin{bmatrix} -2&0 \\ 3&-1 \\ -3&2 \\ 5&-4 \end{bmatrix}

Write the dual of the following LPP:
Maximize z = 2x1 + x2
Subject to x1 + 5x2 < 10
                x1 + 3x2 > 6
                2x1 + 2x2 < 8
                 x2 > 0, x1 is unrestricted in sign.

Solve the (4X3) game with pay off matrix.
A = \begin{bmatrix} 8 &5 &8 \\ 8&6 &5 \\ 7&4 &5 \\ 6&5 & 6 \end{bmatrix}
At each stage, clearly explain the steps involved.

Which of the following statements are true or false? Give reasons for your answer.
i) The number of basic variables in a feasible solution of a transportation problem with m sources and n destinations is mn.
ii) An optimal assignment of the assignment problem with cost matrix C is also an optimal assignment of the assignment problem with cost matrix Ct .
iii) (1, 2) is an optimal solution to the following LPP:
Max Z = 2x + 4x
subject to x1 + 2x2 < 5
x1 + x2 < 4
x1 ,x2 > 0

iv) The intersection of a finite number of convex sets is not a convex set.
v) If value of the 2X2 matrix game \begin{bmatrix} 1 &2 \\ P &4 \end{bmatrix} is 4, then p > 4.

For the following matrix game, write down the equivalent LPPs for solving the game.

           B

A = \begin{bmatrix} -1 &2 \\ 1& 0 \end{bmatrix}

If A =\begin{bmatrix} 1 &5 &3 \\ 2 &5 &7 \end{bmatrix},B = \begin{bmatrix} 1\\3 \end{bmatrix} and C = [1,2] compute A'B, AC, B'A + CB, whenever defined. If you think any of these is not defined, give reason for saying so.

Find an initial basic feasible solution to the following transportation problem by the North-West corner method. Check whether your solution is optimal.

6 4 1 5 14
8 9 2 7 16
4 3 6 2 5
6 10 15 4  

 

IGNOU Solved Assignments Assignments Ignou Projects Project Previous Year Solved Exam Papers Notes Notes Sample Question Papers Sample Question Papers
Login
Top
📞
Call Support Instant phone assistance IGNOU MTE 12 2018 - Solve the following game by graphical method. | IGNOU Academy
→
🟢
WhatsApp Chat Fast live messaging
→
Email Us Business enquiries & support
→