Two Banks (Franklin and Lincoln)compete for Customers in the Growing $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Lincoln Bank }$

question 60

Essay

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:
Strategy 1: 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. $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Lincoln Bank }$
$\begin{array}{|c|ccc|}\hline\text{Franklin Bank}&\begin{array}{c}\text { Hillsboro } \\b_{1}\end{array} & \begin{array}{c}\text { Fremont } \\b_{2}\end{array} & \begin{array}{c}\text { Oakdale } \\b_{3}\end{array} \\\hline \text{Hillsboro }a_{1} &4 & 2 & 3 \\\text{Fremont }a_{2} &6 & -2 & -3 \\\text{Oakdale }a_{3} &-1 & 0 & 5 \\\hline\end{array}$ Identify the neighborhood in which each bank should locate a new branch office.What is the value of the game?

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Definitions:

Perpetuity

A type of annuity that pays an infinite series of payments, continuing indefinitely.

Compounded Monthly

Refers to the process where interest is added to the principal balance of a loan or deposit so that the added interest also earns interest from that point on. This compounding occurs every month.

Withdrawals

The act of removing funds from a bank account or investment.

Compounded Monthly

Interest calculation method where the interest earned each month is added to the principal, affecting future interest calculations.