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Roland's Barber Shop and Charley's Barber Shop are both located in the business district of a certain town. Roland estimates that if he raises the price of a haircut by $1, he will increase his market share by 6% if Charley raises his price by the same amount; he will decrease his market share by 1% if Charley holds his price at the same level; and he will decrease his market share by 4% if Charley lowers his price by $1. If Roland keeps his price the same, he will increase his market share by 5% if Charley raises his price by $1; he will keep the same market share if Charley holds the price at the same level; and he will decrease his market share by 2% if Charley lowers his price by $1. Finally, if Roland lowers the price he charges by $1, his market share will increase by 6% if Charley raises his prices by the same amount; he will increase his market share by 4% if Charley holds his price at the same level; and he will increase his market share by 2% if Charley lowers his price by $1. (a) Construct the payoff matrix for this game. (Enter the values as integer percents. So 1% would be entered as 1.) Charley hold raise Roland hold lower raise (b) Is the game strictly determined? Yes No lower (c) If neither party is willing to lower the price he charges for a haircut, what is the optimal strategy for each barber? The optimal strategy for each barber is to raise prices. There is no optimal strategy since the game is not strictly determined. The optimal strategy for Roland is to keep prices the same, while the optimal strategy for Charley is to raise prices. The optimal strategy for each barber is to keep prices the same. The optimal strategy for Roland is to raise his prices, while the optimal strategy for Charley is to keep prices the same.

Roland's Barber Shop and Charley's Barber Shop are both located in the business district of a certain town. Roland estimates that if he raises the price of a haircut by $1, he will increase his market share by 6% if Charley raises his price by the same amount; he will decrease his market share by 1% if Charley holds his price at the same level; and he will decrease his market share by 4% if Charley lowers his price by $1. If Roland keeps his price the same, he will increase his market share by 5% if Charley raises his price by $1; he will keep the same market share if Charley holds the price at the same level; and he will decrease his market share by 2% if Charley lowers his price by $1. Finally, if Roland lowers the price he charges by $1, his market share will increase by 6% if Charley raises his prices by the same amount; he will increase his market share by 4% if Charley holds his price at the same level; and he will increase his market share by 2% if Charley lowers his price by $1. (a) Construct the payoff matrix for this game. (Enter the values as integer percents. So 1% would be entered as 1.) Charley hold raise Roland hold lower raise (b) Is the game strictly determined? Yes No lower (c) If neither party is willing to lower the price he charges for a haircut, what is the optimal strategy for each barber? The optimal strategy for each barber is to raise prices. There is no optimal strategy since the game is not strictly determined. The optimal strategy for Roland is to keep prices the same, while the optimal strategy for Charley is to raise prices. The optimal strategy for each barber is to keep prices the same. The optimal strategy for Roland is to raise his prices, while the optimal strategy for Charley is to keep prices the same.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Roland's Barber Shop and Charley's Barber Shop are both located in the business district of a certain town. Roland estimates that if he raises the price of a haircut by $1, he will increase his market share by 6% if Charley raises his price by the same amount; he will decrease his market share by 1% if Charley holds his price at the same level; and he will decrease his market share by 4% if Charley lowers his price by $1. If Roland keeps his price the same, he will increase his market share by 5% if Charley raises his price by $1; he will keep the same market share if Charley holds the price at the same level; and he will decrease his market share by 2% if Charley lowers his price by $1. Finally, if Roland lowers the price he charges by $1, his market share will increase by 6% if Charley raises his prices by the same amount; he will increase his market share by 4% if Charley holds his price at the same level; and he will increase his market share by 2% if Charley lowers his price by $1. (a) Construct the payoff matrix for this game. (Enter the values as integer percents. So 1% would be entered as 1.) Charley hold Roland raise No hold lower raise (b) Is the game strictly determined? Yes lower (c) If neither party is willing to lower the price he charges for a haircut, what is the optimal strategy for each barber? The optimal strategy for each barber is to raise prices. There is no optimal strategy since the game is not strictly determined. The optimal strategy for Roland is to keep prices the same, while the optimal strategy for Charley is to raise prices. The optimal strategy for each barber is to keep prices the same. The optimal strategy for Roland is to raise his prices, while the optimal strategy for Charley is to keep prices the same.
Transcribed Image Text:Roland's Barber Shop and Charley's Barber Shop are both located in the business district of a certain town. Roland estimates that if he raises the price of a haircut by $1, he will increase his market share by 6% if Charley raises his price by the same amount; he will decrease his market share by 1% if Charley holds his price at the same level; and he will decrease his market share by 4% if Charley lowers his price by $1. If Roland keeps his price the same, he will increase his market share by 5% if Charley raises his price by $1; he will keep the same market share if Charley holds the price at the same level; and he will decrease his market share by 2% if Charley lowers his price by $1. Finally, if Roland lowers the price he charges by $1, his market share will increase by 6% if Charley raises his prices by the same amount; he will increase his market share by 4% if Charley holds his price at the same level; and he will increase his market share by 2% if Charley lowers his price by $1. (a) Construct the payoff matrix for this game. (Enter the values as integer percents. So 1% would be entered as 1.) Charley hold Roland raise No hold lower raise (b) Is the game strictly determined? Yes lower (c) If neither party is willing to lower the price he charges for a haircut, what is the optimal strategy for each barber? The optimal strategy for each barber is to raise prices. There is no optimal strategy since the game is not strictly determined. The optimal strategy for Roland is to keep prices the same, while the optimal strategy for Charley is to raise prices. The optimal strategy for each barber is to keep prices the same. The optimal strategy for Roland is to raise his prices, while the optimal strategy for Charley is to keep prices the same.
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