Chapter 9.4, Problem 23E

MARKET SHARE: Roland`s Barber Shop and Charley's Bather 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 $3\%$ 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 $3\%$ if Charley lowers his price by SI. If Roland keeps his price the same. he will increase his market share by $2\%$ 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 SI. Finally, if Roland lowers the price he charges by $\$1$. his market share will increase by $5\%$ if Charley raises his prices by the same amount; he will increase his market share by $2\%$ if Charley holds his price at the same level; and he will increase his market share by $1\%$ if Charley lowers his price by $1.

a. Construct the payoff matrix for this game.

b. Show that the game is strictly determined.

c. If neither party is willing to lower the price he charges for a haircut, show that both should keep their present price structures.