Explanation Given Information: The provided payoff matrix is: [ − 1 2 − 1 1 − 2 1 3 − 1 0 ] . Formula used: Solve the matrix game as: Step 1: Reduce the provided payoff matrix. Step 2: Make all the entries non negative by addition by a fixed number k and no column should be all zero. Step 3: Write 1 s to the right of and below the matrix, and solve this primal problem with the help of the simplex method. Step 4: Obtain the optical strategies. Column strategy is enlisted below: 1.Express the solution to the primal problem in the form of column vector . 2. Now, divide each entry of the solution vector by p . 3. Insert zeros in position corresponding to the columns deleted during reduction. Row strategy is enlisted below: 1. Express the solution to the dual problem in the form of row vector. 2. Now, divide each entry by p . 3. Insert zeros in positions corresponding to the rows deleted during reduction. Value of the game is expressed as, e = 1 p − k Calculation: Consider the provided payoff matrix is, [ − 1 2 − 1 1 − 2 1 3 − 1 0 ] . Add k = 2 to each entry and put 1 s to the right and be below. Represent this above problem by the matrix as, [ 4 1 1 0 3 1 1 1 2 1 1 0 ] Obtain the corresponding linear programming problem as, Maximize p = x + y , subject to 4 x + y ≤ 1 , 3 y ≤ 1 , x + 2 y ≤ 1 , x ≥ 0 , y ≥ 0 . Solve the above dual problem using the standard simplex method as: x y z s t u p s 4 1 1 1 0 0 0 1 t 0 3 0 0 1 0 0 1 u 1 2 0 0 0 1 0 1 <

7th Edition

ISBN: 9781337280426

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 5, Problem 23RE

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To calculate: The game matrix when the provided payoff matrix is

[−12−11−213−10].

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Chapter 5, Problem 22RE

Chapter 5, Problem 24RE

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Refer to the payoff matrix below: B1 B2 A1 2 -1 A2 -2 3 Determine the optimal strategy for both players and the value of the game.

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Finite Mathematics

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The game matrix when the provided payoff matrix is [ − 1 2 − 1 1 − 2 1 3 − 1 0 ] .

Solution Summary: The author explains how to calculate the matrix game using the simplex method.

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To calculate: The game matrix when the provided payoff matrix is

[−12−11−213−10].

Want to see the full answer?

Chapter 5 Solutions

The game matrix when the provided payoff matrix is [ − 1 2 − 1 1 − 2 1 3 − 1 0 ] .

Solution Summary: The author explains how to calculate the matrix game using the simplex method.

Videos

To calculate: The game matrix when the provided payoff matrix is [−12−11−213−10].

Want to see the full answer?

Chapter 5 Solutions

To calculate: The game matrix when the provided payoff matrix is

[−12−11−213−10].