Chapter 10.1, Problem 46E

Store location Two competing auto parts companies ( $R$ and $C$ ) are trying to decide among three small towns ( $E$, $F$, and $G$ ) for new store locations. All three towns have the same business potential. If both companies operate in the same town, they split the business evenly (payoff is $0$ to both). If, however, they operate in different towns, the store that is closer to the third town will get all of that town’s business. For example, if $R$ operates in $E$ and $C$ in $E$, the payoff is $1$ ( $R$ $E$ has gained one town). If. on the other hand. operates in $F$ and $C$ in, the payoff is $1$ ( $R$ has lost one town to $C$ ). Write the payoff matrix, find all saddle values, and indicate optimal strategies for both stores.