(a) Explanation Given Information: The provided payoff matrix is, P = [ − 2 − 1 − 1 − 3 ] Formula used: Steps to find the expected payoff from mixed strategies R and C. Step 1: As a row matrix R write the mixed strategy for row player. Step 2: As a column matrix C write the mixed strategy for column player. Step 3: Calculate the product RPC , it is 1 × 1 matrix and its entry is e (expected payoff), where P represents the payoff matrix. Calculation: Consider the provided payoff matrix, P = [ − 2 − 1 − 1 − 3 ] Now write the general row strategy, R = [ x y ] For the optimal row strategy take x + y = 1 , so R = [ x 1 − x ] And consider C = [ 1 0 ] T , Now calculate the product RPC , which is e (expected payoff), e = R P C = [ x 1 − x ] [ − 2 − 1 − 1 − 3 ] [ 1 0 ] T = [ x 1 − x ] [ − 2 − 1 − 1 − 3 ] [ 1 0 ] = − 2 x − ( 1 − x ) Now simplify further, e = − 2 x − 1 + x = − x − 1 Now consider C = [ 0 1 ] T , And calculate the product RPC , which is f (expected payoff), f = R P C = [ x 1 − x ] [ (b) To determine To calculate: The optimal mixed column strategy for the provided payoff matrix. P = [ − 2 − 1 − 1 − 3 ] (c) To determine To calculate: The value of the game that is expected for the provided payoff matrix. P = [ − 2 − 1 − 1 − 3 ]

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 5.4, Problem 24E

(a)

To determine

To calculate: The optimal mixed row strategy for the provided payoff matrix.

P=[−2−1−1−3]

(b)

To determine

To calculate: The optimal mixed column strategy for the provided payoff matrix.

P=[−2−1−1−3]

(c)

To determine

To calculate: The value of the game that is expected for the provided payoff matrix.

P=[−2−1−1−3]

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Chapter 5.4, Problem 23E

Chapter 5.4, Problem 25E

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The optimal mixed row strategy for the provided payoff matrix. P = [ − 2 − 1 − 1 − 3 ]

Solution Summary: The author explains how to calculate the optimal mixed row strategy for the provided payoff matrix.

Videos

To calculate: The optimal mixed row strategy for the provided payoff matrix.

P=[−2−1−1−3]

To calculate: The optimal mixed column strategy for the provided payoff matrix.

P=[−2−1−1−3]

To calculate: The value of the game that is expected for the provided payoff matrix.

P=[−2−1−1−3]

Want to see the full answer?

Chapter 5 Solutions

The optimal mixed row strategy for the provided payoff matrix. P = [ − 2 − 1 − 1 − 3 ]

Solution Summary: The author explains how to calculate the optimal mixed row strategy for the provided payoff matrix.

Videos

To calculate: The optimal mixed row strategy for the provided payoff matrix. P=[−2−1−1−3]

To calculate: The optimal mixed column strategy for the provided payoff matrix. P=[−2−1−1−3]

To calculate: The value of the game that is expected for the provided payoff matrix. P=[−2−1−1−3]

Want to see the full answer?

Chapter 5 Solutions

To calculate: The optimal mixed row strategy for the provided payoff matrix.

P=[−2−1−1−3]

To calculate: The optimal mixed column strategy for the provided payoff matrix.

P=[−2−1−1−3]

To calculate: The value of the game that is expected for the provided payoff matrix.

P=[−2−1−1−3]