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 +
______ _______ ___ ____ ______ __________.
___ __________ _____ _______ ____ _____ _________.
_____ ___ ___ ___ ____.
___ ________ ______ ______ ______ ___ _________ _________ ________ ________.
________ _______ _________ _________ __________.
______ _________ __________ ______ ___ _______ ___ __________ _________ ______ __________ ___.
__________ _______ __________ _______ ______.
_____ ____ _________ _______ ______ _______ _____ ____ __________.
___ __________ ______ _________ ________ ____.
___ ____ ______ ____ ______ ____ _______ ________ _______ ____ _____.
_______ ____ ____ _______ ____ ______ ___ _________.
_________ ____ ________ ___ ______ __________ __________.
_________ ______ ______ ____ ___ _______ _________ ___ ___ __________ ______ ___.
____ _________ __________ ______ ____ _______.
_________ _______ ________ ______ ____ _____ ____ ______ ____ ______.
______ _________ ____ _______ __________ _________ _______ _____ ___ _______ ________.
_______ _______ _________ ___ _______ ________ ________ ___.
______ __________ __________ ________ ____ ________ _____ ____ _________.
_________ ____ __________ ____ ___ ______ ________ _______ _________.
____ ______ ___ _____ __________ ____ ________ ____ ____.
_____ _________ ____ __________ ________.
____ ______ __________ __________ ____ ______ _________.
________ __________ ___ _______ _________ _____ _____.
___ ______ _________ _________ _______ ________ ________ ______ ______ __________ _________ __________.
___ __________ _______ _____ ____ ______.
_________ _____ _______ ___ _____ ___ ________.
_____ ____ ___ ________ _____ _____ ____ _______ _____ __________.
________ _______ ____ ___ ____.
_______ _________ ________ __________ _________ _________ ____ _______ __________ _________ __________ _____.
________ __________ ________ ________ _________ _______ _______ ___ _________ ________ __________.
___ ___ _______ _______ ___ ________.
_______ _______ ________ ________ ___ ___ __________ _________ _____ __________.
_________ __________ _______ ___ ___ ______ _________ __________.
________ ____ ______ __________ ______ _______ _______ ______ _________.
________ ________ ______ __________ ____ _______ _________ ______ _______ ____ ____ __________.
_________ ________ _____ _________ __________ ___ __________ _____.
______ _________ ______ _____ __________ ___.
__________ _______ __________ ___ __________.
_____ _______ ___ __________ ________ ________ ____.
__________ __________ __________ ____ _____.
_________ ____ ________ ______ ________ _______ ______ ________.
____ ___ _______ _______ ____ _______ ___ ______ ________ ______.
___ __________ _________ __________ _______ ______ ________ _____.
_____ ___ ___ _______ ________.
___ ___ ___ _________ ________ _________.
________ _____ ___ ________ _________ _________ _________ ___ _________ _____ __________ ________.
_________ ____ ____ _____ __________ __________ ____ _________ _____ __________.
_____ ______ _______ _______ ___ ________.
________ _______ ________ ______ ______.
__________ ________ ________ ____ ______ _______ ______.
_____ __________ _________ ____ ____ ________ ____ _______ __________ _______ _________ _____.
_____ _______ ___ ____ _______ ______.
____ _________ _______ _________ _____ _________ _________ _____.
_______ _____ __________ _______ _______.
_______ ____ _______ ____ _________ _________ ___ ____ ___ ____ ________.
________ ________ ______ _________ _________ ________ _________ ______ ___ ________.
______ _______ __________ __________ __________ _____ _______ _________ _____ _____.
___ ________ ______ _____ _________ ________ _________.
___ ______ __________ _______ ______ ___.
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

Is the set of vectors{(1,2,3),(3,4,1),(2,3,2)} linearly independent? Give reason for the answer.

A businessman needs 5 cabinets, 12 desks and 18 shelves cleaned out. He has two part time employees, Rashid and Ruby. Ruby can clean 1 cabinet, 3 desks and 3 shelves in a day while Rashid can clean 1 cabinet, 2 desks and 6 shelves in one day. Rashid is paid Rs.22 per day and Ruby is paid Rs.25 per day. In order to minimize the cleaning costs, for how many days should Rashid and Ruby be employed? Formulate the problem as a linear programming problem and find its solution by simplex method.

Prove that the dual of dual of a LPP is primal LPP.

Using dominance property, solve the game whose payoff matrix is

\begin{bmatrix} 4&2 &4 &0 \\ 3&4 &2 &4 \\ 4&2 &4 &0 \\ 0& 4& 0&8 \end{bmatrix}

Solve the following LPP using two-phase method.
Min Z = -3x - 2y - 2z
s.t. 5x + 7y + 4z > 7
- 4x + 7y + 5z > -2
3x + 4y - 6z > 29 / 7
x, y, z > 0.

A firm manufactures pills in two sizes A and B. A contains 2 grains of aspirin, 5 grains of bicarbonate and 1 grains of codeine. B contains 1 grain of aspirin, 8 grains of bicarbonate and 6 grains of aspirin, 74 grains of bicarbonate and 24 grains of codeine for providing immediate effect. It is required to determine the least number of pills a patient should take to get immediate relief. Formulate the problem as a standard LPP and solve it graphically.

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.

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
→