M$4-15$

Shoe Town and Fancy Foot are both vying for more share of the market. If Shoe Town

does no advertising, it will not lose any share of the market if Fancy Foot does nothing. It

will lose $2\%$ of the market if Fancy Foot invests $$10,000\mathrm{.}00$ in advertising, and it will lose

$5\%$ of the market if Fancy Foot invests $$20,000\mathrm{.}00$ in advertising. On the other hand, if

Shoe Town invests $$15,000\mathrm{.}00$ in advertising, it will gain $3\%$ of the market if Fancy Foot

does nothing. It will gain $1\%$ of the market if Fancy Foot invests $$10,000\mathrm{.}00$ in advertising.

It will lose $1\%$ if Fancy Foot invests $$20,000\mathrm{.}00$ in advertising.

a$)$ Develop a payoff table for this problem.

b$)$ Determine the various strategies using the computer. $($Use QM for Windows$).$

c$)$ How would you determine the value of the game?