Explanation Given Information: The payoff matrix, Abercrom A 30 % off 5 0 % off Abercrom B Do Nothing Increase prices [ − 60 − 40 30 − 50 ] Abercrom A have 20% chance to opt for 30 % off sale and 80 % chance for 50 % off sale and there is 50 % chance that Abercrom B will increase prices. Formula used: When a matrix has m rows and n columns, then the matrix is said to have dimension of m × n . According to the product rule of matrices, the matrix X with dimension m × n and the matrix Y with dimension n × k , the product XY is the matrix of dimension m × k and ij th entry of AB is the sum of product of corresponding entries of row i of X and column j of Y . Steps to find the expected payoff from mixed strategies, Step 1: Write the row matrix R , which is the mixed strategy of the row player. Step 2: Write the column matrix C , which is the mixed strategy of the column player. Step 3: Find the product of row matrix R, column matrix C and payoff matrix P . The resultant entry of the 1 × 1 matrix is the expected payoff. Calculation: Consider the payoff matrix, Abercrom A 30 % off 5 0 % off Abercrom B Do Nothing Increase prices [ − 60 − 40 30 − 50 ] Here, the row matrix represent the chances that Abercrom B will increase prices or do nothing and column matrix represent the chances that Abercrom A will launch either a 30 % off everything or 50 % off everything sale. As Abercrom A have 20% chance to opt for 30 % off sale and 80 % chance for 50 % off sale and there is 50 % chance that Abercrom B will increase prices. Thus, R = [ 0.50 0.50 ] and C = [ 0.20 0.80 ] . Therefore, the expected payoff, e = R P C = [ 0.50 0.50 ] [ − 60 − 40 30 − 50 ] [ 0.20 0.80 ] For matrix R , since, number of rows in [ 0.50 0.50 ] is 1 and number of columns is 2 , thus the dimension of [ 0

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ISBN: 9781337280426

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 4.4, Problem 33E

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To calculate: The expected effect on customer base of Abercrom B where Abercrom A have 20% chance to opt for 30% off sale and 80% chance for 50% off sale and there is 50% chance that Abercrom B will increase prices.

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Chapter 4.4, Problem 32E

Chapter 4.4, Problem 34E

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The expected effect on customer base of Abercrom B where Abercrom A have 20% chance to opt for 30 % off sale and 80 % chance for 50 % off sale and there is 50 % chance that Abercrom B will increase prices.

Solution Summary: The author calculates the expected effect on customer base of Abercrom B where they will lose 39 customers.

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To calculate: The expected effect on customer base of Abercrom B where Abercrom A have 20% chance to opt for 30% off sale and 80% chance for 50% off sale and there is 50% chance that Abercrom B will increase prices.

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