Chapter 11.1, Problem 43E

Price war a small town on a major highway has only two gas stations: station $R$, a major brand station, and station $C$ an independent. A market research firm provided the following payoff matrix, where each entry indicates the percentage of customers who go to station $R$ for the indicated prices per gallon of unleaded gasoline. Find saddle values and optimal strategies for each company.

$\begin{array}{l}\text{ Station }C\\ \begin{array}{cc}\$1.35& \$1.40\end{array}\\ \text{Station }R\begin{array}{c}\$1.40\\ \$1.45\end{array}\left[\begin{array}{cc}50\%& 70\%\\ 40\%& 50\%\end{array}\right]\end{array}$