Two men’s clothing stores that compete for most of the market in a small town in Ohio and will choose their weekly advertising levels sequentially. The newspaper advertising department calls the clothing stores in alphabetical order to find out how much advertising each firm wishes to buy. Somehow — and nobody at the newspaper knows exactly how this happens — Arbuckle’s advertising decision “leaks out” to Mr. B’s, which then knows Arbuckle’s advertising decision when it makes its advertising decision for the week. The following payoff table facing the two firms, Arbuckle & Son and Mr. B’s, shows the weekly profit outcomes for the various advertising decision combinations. The payoff table is common knowledge. Use this payoff table to construct the appropriate sequential decision on the blank game tree provided below. If the manager at Arbuckle and Son employs the roll-back method to make the advertising decision for Arbuckle, the likely outcome will be: Multiple Choice $5,000 of weekly profit for Arbuckle and $5,000 of weekly profit for Mr. B’s. $5,000 of weekly profit for Arbuckle and $3,000 of weekly profit for Mr. B’s. $3,000 of weekly profit for Arbuckle and $5,000 of weekly profit for Mr. B’s. $3,500 of weekly profit for Arbuckle and $3,500 of weekly profit for Mr. B’s.
Two men’s clothing stores that compete for most of the market in a small town in Ohio and will choose their weekly advertising levels sequentially. The newspaper advertising department calls the clothing stores in alphabetical order to find out how much advertising each firm wishes to buy. Somehow — and nobody at the newspaper knows exactly how this happens — Arbuckle’s advertising decision “leaks out” to Mr. B’s, which then knows Arbuckle’s advertising decision when it makes its advertising decision for the week. The following payoff table facing the two firms, Arbuckle & Son and Mr. B’s, shows the weekly profit outcomes for the various advertising decision combinations. The payoff table is common knowledge. Use this payoff table to construct the appropriate sequential decision on the blank game tree provided below. If the manager at Arbuckle and Son employs the roll-back method to make the advertising decision for Arbuckle, the likely outcome will be:
Multiple Choice
$5,000 of weekly profit for Arbuckle and $5,000 of weekly profit for Mr. B’s.
$5,000 of weekly profit for Arbuckle and $3,000 of weekly profit for Mr. B’s.
$3,000 of weekly profit for Arbuckle and $5,000 of weekly profit for Mr. B’s.
$3,500 of weekly profit for Arbuckle and $3,500 of weekly profit for Mr. B’s.
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