Two banks (Franklin and Lincoln) compete for customers in the growing city of Logantown. Both banks are considering opening a branch office in one of three new neighborhoods:

Hillsboro, Fremont, or Oakdale. The strategies, assumed to be the same for both banks, are:

Strategy1: Open a branch office in the Hillsboro neighborhood.

Strategy 2: Open a branch office in the Fremont neighborhood.

Strategy 3: Open a branch office in the Oakdale neighborhood.

Values in the payoff table below indicate the gain (or loss) of customers (in thousands) for Franklin Bank based on the strategies selected by the two banks.

Lincoln Bank

Franklin Bank Hillsboro Fremont Oakdale

Hillsboro 20,20 35,25 35,20

Fremont 30,25 15,15 30,20

Oakdale 20,25 20,25 10,10

Is there a pure strategy for this game? If so, what is it? If not, identify the potential solutions (neighborhood in which each bank should locate a new branch office).