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 F, the payoff is 1 (R has gained one town). If, on the other hand, R operates in F and C in E, 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.

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10 kilometers E G 14 kilometers 20 kilometers F