Two banks (Franklin and Lincoln) compete for customers in the growing city of Logan town. Both banks are considering opening a branch office in one of three new neighbour hoods: Hillsboro, Fremont, or Oakdale. The strategies, assumed to be the same for both banks, are:
Strategy1: Open a branch office in the Hillsboro neighbourhood.
Strategy 2: Open a branch office in the Fremont neighbourhood.
Strategy 3: Open a branch office in the Oakdale neighbourhood.
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 (neighbourhood in which each bank should locate a new branch office).