Explanation Given Information: The row player decides to play the mixed strategy [ 0.5 0.5 ] by alternating two strategies, play the first strategy on the odd-numbered moves and the second on the even-numbered moves. Consider the row player decides to play the mixed strategy [ 0.5 0.5 ] by alternating two strategies, play the first strategy on the odd-numbered moves and the second on the even-numbered moves. Since, the row player strictly alternates the moves, the column player can easily guess the strategy used by the row player. Thus, the column player will chose a pure strategy accordingly and row player will get a lower payoff each time. For example, Consider a game with the payoff matrix a b A B [ 1 0 0 1 ] . Let the row player use the strategy R = [ 0.5 0.5 ] and let C = [ x y ] be the column matrix for the other player. Now, the expected payoff e of the game is product of the matrices in the order RPC , where R is the row matrix, P is the payoff Matrix and C is the column matrix. Consider the product, e = R P C = [ 0.5 0.5 ] [ 1 0 0 1 ] [ x y ] For matrices A with dimension m × n and B with dimension k × l , the product AB is defined if the number of columns in A equal number of columns in B , n = k . For matrix R , since number of rows in [ 0.5 0.5 ] is 1 and number of columns is 2. Thus, dimension of [ 0.5 0.5 ] is 1 × 2 . For matrix P , since number of rows in [ 1 0 0 1 ] is 2 and number of columns is 2 . Thus, dimension of [ 1 0 0 1 ] is 2 × 2 . For matrix C , since number of rows in [ x y ] is 2 and number of columns is 1. Thus, dimension of [ x y ] is 2 × 1 . As the number of columns in R is equal to the number of rows in P , the product RP is defined

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 57E

To determine

The reason why a decision to play the mixed strategy [0.50.5] by alternating two strategies, play the first strategy on the odd-numbered moves and the second on the even-numbered moves is wrong.

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Chapter 5.4, Problem 56E

Chapter 5.4, Problem 58E

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Chapter 5 Solutions

Finite Mathematics and Applied Calculus (MindTap Course List)

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Ch. 5.1 - Solve for x,y,z,andw. [HINT: See Example 1.]...Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - In Exercises 1320, evaluate the given expression....Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - In Exercises 2128, evaluate the given expression....Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - In Exercises 2128, evaluate the given expression....Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - In Exercises 2936, use technology to evaluate the...Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Sales The following table shows the number of Mac...Ch. 5.1 - Home Prices The following table shows median home...Ch. 5.1 - Inventory The Left Coast Bookstore chain has two...Ch. 5.1 - Inventory The Left Coast Bookstore chain discussed...Ch. 5.1 - Prob. 41E Ch. 5.1 - Revenue The following spreadsheet gives annual...Ch. 5.1 - 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The reason why a decision to play the mixed strategy [ 0.5 0.5 ] by alternating two strategies, play the first strategy on the odd-numbered moves and the second on the even-numbered moves is wrong.

Solution Summary: The author explains that a row player's decision to play the mixed strategy left[cc0.5] is wrong, since the column player alternates the two strategies strictly,

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The reason why a decision to play the mixed strategy [0.50.5] by alternating two strategies, play the first strategy on the odd-numbered moves and the second on the even-numbered moves is wrong.

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Chapter 5 Solutions